Next Issue
Volume 11, December
Previous Issue
Volume 11, October
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
2.0
Journals
Axioms
Volume 11
Issue 11
share announcement

Axioms, Volume 11, Issue 11 (November 2022) – 81 articles

Cover Story (view full-size image): This work is aimed at closed-form results in a GI-X/G-NSV/1 queue under occasional maintenance performed by the server. Upon his return, the server rests unless the queue raised to at least N units (N-Policy). Server’s maintenance time is initially set as T, but it is continually reduced due to projected random services of new units entering the system. Obtained is the maintenance time distribution using the first passage time analysis of random walks on non-rectangular stochastic grids. Further employed semi-regenerative analysis targeted the continuous time parameter queue that in turn produced optimal values of T and threshold N. View this paper
  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
21 pages, 977 KiB  
Article
Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment
by Qazi Shoeb Ahmad, Mohammad Faisal Khan and Naeem Ahmad
Axioms 2022, 11(11), 659; https://doi.org/10.3390/axioms11110659 - 21 Nov 2022
Cited by 3 | Viewed by 1500
Abstract
The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it [...] Read more.
The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it uses fewer calculations and analyses while maintaining good, acceptable consistency ratio values. A multi-choice best–worst method (MCBWM), which considers several options for pairwise comparison of preferences between the criteria, has recently been developed. The experts are given the option to select values from several comparison scales. The MCBWM technique has been shown to be better. Presenting the options for which an optimal solution has been found simplifies the calculation and establishes the ideal weight values. This study proposes two different mathematical programming models for solving multi-criteria decision-making problems having multiple decision-makers. The two methods are proposed considering the multi-choice uncertainty assumption in pairwise criteria comparisons. Additionally, it considers the best–worst method as the base model. The multi-choice uncertainty is applied to determine the best choice out of multiple choices. It gives a real-life scenario to the decision-making problems. Although there are many other forms of uncertainty, such as fuzzy, intuitionistic fuzzy, neutrosophic, probabilistic, etc., it focuses on choices instead of ambiguity in terms of the probabilistic or fuzzy nature of parameters. The parameter considered as multi-choice is the pairwise comparison. These parameters are handled by applying the Lagrange interpolating polynomial method. The proposed models are novel in terms of their mathematical structure and group decision-making approach. The models are formulated and further validated by solving numerical examples. It provides a framework for solving mcdm problems where the weightage to the decision-makers is also incorporated. The CR values for all the models of example 1 and 2, and the case study has been found acceptable. Full article
(This article belongs to the Special Issue Multiple-Criteria Decision Making II)
►▼ Show Figures

Figure 1

13 pages, 598 KiB  
Article
Hypercomplex Systems and Non-Gaussian Stochastic Solutions with Some Numerical Simulation of χ-Wick-Type (2 + 1)-D C-KdV Equations
by Mohammed Zakarya, Mahmoud A. Abd-Rabo and Ghada AlNemer
Axioms 2022, 11(11), 658; https://doi.org/10.3390/axioms11110658 - 21 Nov 2022
Cited by 1 | Viewed by 1222
Abstract
In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product. White noise functional solutions (WNFS) are presented with the homogeneous equilibrium principle, [...] Read more.
In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product. White noise functional solutions (WNFS) are presented with the homogeneous equilibrium principle, Hermite transform (HT), and technicality via the F-expansion procedure. By means of the direct connection between the theory of hypercomplex systems (HCS) and white noise analysis (WNA), we establish non-Gaussian white noise (NGWN) by studying stochastic partial differential equations (PDEs) with NG-parameters. So, by using the F-expansion method we present multiples of exact and stochastic families from variable coefficients of travelling wave and stochastic NG-functional solutions of (2 + 1)-D C-KdV equations. These solutions are Jacobi elliptic functions (JEF), trigonometric, and hyperbolic forms, respectively. Full article
(This article belongs to the Special Issue Recent Advances in Stochastic Differential Equations)
►▼ Show Figures

Figure 1

9 pages, 1519 KiB  
Article
Computation of the Deuteron Mass and Force Unification via the Rotating Lepton Model
by Constantinos G. Vayenas, Dimitrios Grigoriou, Dionysios Tsousis, Konstantinos Parisis and Elias C. Aifantis
Axioms 2022, 11(11), 657; https://doi.org/10.3390/axioms11110657 - 20 Nov 2022
Cited by 2 | Viewed by 1865
Abstract
The rotating lepton model (RLM), which is a 2D Bohr-type model of three gravitating rotating neutrinos, combining Newton’s gravitational law, special relativity, and the de Broglie equation of quantum mechanics, and which has already been used to model successfully quarks and the strong [...] Read more.
The rotating lepton model (RLM), which is a 2D Bohr-type model of three gravitating rotating neutrinos, combining Newton’s gravitational law, special relativity, and the de Broglie equation of quantum mechanics, and which has already been used to model successfully quarks and the strong force in several hadrons, has been extended to 3D and to six rotating neutrinos located at the vertices of a normal triangular octahedron in order to compute the Lorentz factors, gamma, of the six neutrinos and, thus, to compute the total energy and mass of the deuteron, which is the lightest nucleus. The computation includes no adjustable parameters, and the computed deuteron mass agrees within 0.05% with the experimental mass value. This very good agreement suggests that, similarly to the strong force in hadrons, the nuclear force in nuclei can also be modeled as relativistic gravity. This implies that, via the combination of special relativity and quantum mechanics, the Newtonian gravity gets unified with the strong force, including the residual strong force. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
►▼ Show Figures

Figure 1

21 pages, 4660 KiB  
Article
A Unified Asymptotic Theory of Supersonic, Transonic, and Hypersonic Far Fields
by Lung-Jieh Yang and Chao-Kang Feng
Axioms 2022, 11(11), 656; https://doi.org/10.3390/axioms11110656 - 19 Nov 2022
Viewed by 1056
Abstract
The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such [...] Read more.
The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such a problem with far fields was solved by W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This far field small disturbance theory is reexamined in this study first by using asymptotic expansion theory. A systematic approach is adopted to obtain the nonlinear Burgers’ equation for supersonic far fields. We also use the similarity method to solve this boundary value problem (BVP) of the inviscid Burgers’ equation and obtain the nonlinear flow patterns, including the jump condition for the shock wave. Secondly, the transonic and hypersonic far field equations were obtained from the supersonic Burgers’ equation by stretching the coordinate in the y direction and considering an expansion of the freestream Mach number in terms of the transonic and hypersonic similarity parameters. The mathematical structures of the far fields of the supersonic, transonic, and hypersonic flows are unified to be the same. The similar far field flow patterns including the shock positions of a parabolic airfoil for the supersonic, transonic, and hypersonic flow regimes are exemplified and discussed. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Chaos and Their Applications to Engineering and Science)
►▼ Show Figures

Figure 1

13 pages, 272 KiB  
Article
Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions
by Mohammad Faisal Khan, Shahid Khan, Saqib Hussain, Maslina Darus and Khaled Matarneh
Axioms 2022, 11(11), 655; https://doi.org/10.3390/axioms11110655 - 18 Nov 2022
Cited by 2 | Viewed by 1096
Abstract
Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fractional differential operator and the Mittag-Leffler [...] Read more.
Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fractional differential operator and the Mittag-Leffler functions to formulate and arrange a new operator of fractional calculus. We define a new class of normalized analytic functions by means of a newly defined fractional operator and discuss some of its interesting geometric properties in open unit disk. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory)
20 pages, 729 KiB  
Article
Fractional Clique Collocation Technique for Numerical Simulations of Fractional-Order Brusselator Chemical Model
by Mohammad Izadi and Hari Mohan Srivastava
Axioms 2022, 11(11), 654; https://doi.org/10.3390/axioms11110654 - 18 Nov 2022
Cited by 13 | Viewed by 1312
Abstract
The primary focus of this research study is in the development of an effective hybrid matrix method to solve a class of nonlinear systems of equations of fractional order arising in the modeling of autocatalytic chemical reaction problems. The fractional operator is considered [...] Read more.
The primary focus of this research study is in the development of an effective hybrid matrix method to solve a class of nonlinear systems of equations of fractional order arising in the modeling of autocatalytic chemical reaction problems. The fractional operator is considered in the sense of Liouville–Caputo. The proposed approach relies on the combination of the quasi-linearization technique and the spectral collocation strategy based on generalized clique bases. The main feature of the hybrid approach is that it converts the governing nonlinear fractional-order systems into a linear algebraic system of equations, which is solved in each iteration. In a weighted L2 norm, we prove the error and convergence analysis of the proposed algorithm. By using various model parameters in the numerical examples, we show the computational efficacy as well as the accuracy of our approach. Comparisons with existing available schemes show the high accuracy and robustness of the designed hybrid matrix collocation technique. Full article
(This article belongs to the Special Issue Theory of Functions and Applications)
►▼ Show Figures

Figure 1

9 pages, 265 KiB  
Article
Application of the Averaging Method to the Optimal Control Problem of Non-Linear Differential Inclusions on the Finite Interval
by Tetiana Zhuk, Nina Kasimova and Anton Ryzhov
Axioms 2022, 11(11), 653; https://doi.org/10.3390/axioms11110653 - 17 Nov 2022
Cited by 1 | Viewed by 1015
Abstract
In this paper, we use the averaging method to find an approximate solution for the optimal control of non-linear differential inclusions with fast-oscillating coefficients on a finite time interval. Full article
(This article belongs to the Special Issue Mathematical Control and Applications)
9 pages, 293 KiB  
Article
New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials
by Mucahit Buyankara, Murat Çağlar and Luminiţa-Ioana Cotîrlă
Axioms 2022, 11(11), 652; https://doi.org/10.3390/axioms11110652 - 17 Nov 2022
Cited by 9 | Viewed by 1553
Abstract
In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z∈C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2, [...] Read more.
In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z∈C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 and Fekete–Szegö inequalities a3−μa22 for these new subclasses. Full article
(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)
20 pages, 907 KiB  
Article
Computational Framework of the SVIR Epidemic Model with a Non-Linear Saturation Incidence Rate
by Attaullah, Adil Khurshaid, Zeeshan, Sultan Alyobi, Mansour F. Yassen and Din Prathumwan
Axioms 2022, 11(11), 651; https://doi.org/10.3390/axioms11110651 - 17 Nov 2022
Cited by 3 | Viewed by 2295
Abstract
In this study, we developed an autonomous non-linear epidemic model for the transmission dynamics of susceptible, vaccinated, infected, and recovered individuals (SVIR model) with non-linear saturation incidence and vaccination rates. The non-linear saturation incidence rate significantly reduces the death ratio of infected individuals [...] Read more.
In this study, we developed an autonomous non-linear epidemic model for the transmission dynamics of susceptible, vaccinated, infected, and recovered individuals (SVIR model) with non-linear saturation incidence and vaccination rates. The non-linear saturation incidence rate significantly reduces the death ratio of infected individuals by increasing human immunity. We discuss a detailed explanation of the model equilibrium, its basic reproduction number R0, local stability, and global stability. The disease-free equilibrium is observed to be stable if R0<1, while the endemic equilibrium exists and the disease exists permanently in the population if R0>1. To approximate the solution of the model, the well-known Runge–Kutta (RK4) methodology is utilized. The implications of numerous parameters on the population dynamics of susceptible, vaccinated, infected, and recovered individuals are addressed. We discovered that increasing the value of the disease-included death rate ψ has a negative impact on those affected, while it has a positive impact on other populations. Furthermore, the value of interaction between vaccinated and infected λ2 has a decreasing impact on vulnerable and vaccinated people, while increasing in other populations. On the other hand, the model is solved using Euler and Euler-modified techniques, and the results are compared numerically and graphically. The quantitative computations demonstrate that the RK4 method provides very precise solutions compared to the other approaches. The results show that the suggested SVIR model that approximates the solution method is accurate and useful. Full article
(This article belongs to the Special Issue Mathematical Modelling and Applications)
►▼ Show Figures

Figure 1

14 pages, 334 KiB  
Article
Six-Dimensional Space with Symmetric Signature and Some Properties of Elementary Particles
by Nikolay Popov and Ivan Matveev
Axioms 2022, 11(11), 650; https://doi.org/10.3390/axioms11110650 - 17 Nov 2022
Cited by 2 | Viewed by 1425
Abstract
The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, [...] Read more.
The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, and hypercharge, are expressed through the symmetries of this space. The symmetries are brought out by the various representation of the metric in E3,3 with the aid of spinors and hyperbolic complex numbers. The properties of the metric allow predicting the number of quarks equal to 18. The violation of strong conservation laws in weak interactions is treated through compactifying the three-dimensional temporal subspace at the subparticle scale into single-dimensional time at bigger scales, which reduces symmetry from the spherical to axial type. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
►▼ Show Figures

Figure 1

12 pages, 414 KiB  
Article
Probing the Oscillatory Behavior of Internet Game Addiction via Diffusion PDE Model
by Kaihong Zhao
Axioms 2022, 11(11), 649; https://doi.org/10.3390/axioms11110649 - 16 Nov 2022
Cited by 11 | Viewed by 1197
Abstract
We establish a non-linear diffusion partial differential equation (PDE) model to depict the dynamic mechanism of Internet gaming disorder (IGD). By constructing appropriate super- and sub-solutions and applying Schauder’s fixed point theorem and continuation method, we study the existence and asymptotic stability of [...] Read more.
We establish a non-linear diffusion partial differential equation (PDE) model to depict the dynamic mechanism of Internet gaming disorder (IGD). By constructing appropriate super- and sub-solutions and applying Schauder’s fixed point theorem and continuation method, we study the existence and asymptotic stability of traveling wave solutions to probe into the oscillating behavior of IGD. An example is numerically simulated to examine the correctness of our outcomes. Full article
(This article belongs to the Special Issue Differential Equations in Applied Mathematics)
►▼ Show Figures

Figure 1

16 pages, 317 KiB  
Article
Optimality Conditions and Dualities for Robust Efficient Solutions of Uncertain Set-Valued Optimization with Set-Order Relations
by Yuwen Zhai, Qilin Wang and Tian Tang
Axioms 2022, 11(11), 648; https://doi.org/10.3390/axioms11110648 - 16 Nov 2022
Cited by 2 | Viewed by 1350
Abstract
In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on. By the new subdifferential and its properties, we establish a necessary and sufficient optimality condition of set-based robust efficient [...] Read more.
In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on. By the new subdifferential and its properties, we establish a necessary and sufficient optimality condition of set-based robust efficient solutions for the uncertain set-valued optimization problem. We also introduce a Wolfe type dual problem of the uncertain set-valued optimization problem. Finally, we establish the robust weak duality theorem and the robust strong duality theorem between the uncertain set-valued optimization problem and its robust dual problem. Several main results extend to the corresponding ones in the literature. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
31 pages, 440 KiB  
Article
Justification of Direct Scheme for Asymptotic Solving Three-Tempo Linear-Quadratic Control Problems under Weak Nonlinear Perturbations
by Galina Kurina and Margarita Kalashnikova
Axioms 2022, 11(11), 647; https://doi.org/10.3390/axioms11110647 - 16 Nov 2022
Cited by 3 | Viewed by 1075
Abstract
The paper deals with an application of the direct scheme method, consisting of immediately substituting a postulated asymptotic solution into a problem condition and determining a series of control problems for finding asymptotics terms, for asymptotics construction of a solution of a weakly [...] Read more.
The paper deals with an application of the direct scheme method, consisting of immediately substituting a postulated asymptotic solution into a problem condition and determining a series of control problems for finding asymptotics terms, for asymptotics construction of a solution of a weakly nonlinearly perturbed linear-quadratic optimal control problem with three-tempo state variables. For the first time, explicit formulas for linear-quadratic optimal control problems, from which all terms of the asymptotic expansion are found, are justified, and the estimates of the proximity between the asymptotic and exact solutions are proved for the control, state trajectory, and minimized functional. Non-increasing of the minimized functional, if a next approximation to the optimal control is used, following from the proposed algorithm of the asymptotics construction, is also established. Full article
(This article belongs to the Special Issue Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution)
24 pages, 482 KiB  
Article
Modelling Coronavirus and Larvae Pyrausta Data: A Discrete Binomial Exponential II Distribution with Properties, Classical and Bayesian Estimation
by Mohamed S. Eliwa, Abhishek Tyagi, Bader Almohaimeed and Mahmoud El-Morshedy
Axioms 2022, 11(11), 646; https://doi.org/10.3390/axioms11110646 - 16 Nov 2022
Cited by 5 | Viewed by 1228
Abstract
In this article, we propose the discrete version of the binomial exponential II distribution for modelling count data. Some of its statistical properties including hazard rate function, mode, moments, skewness, kurtosis, and index of dispersion are derived. The shape of the failure rate [...] Read more.
In this article, we propose the discrete version of the binomial exponential II distribution for modelling count data. Some of its statistical properties including hazard rate function, mode, moments, skewness, kurtosis, and index of dispersion are derived. The shape of the failure rate function is increasing. Moreover, the proposed model is appropriate for modelling equi-, over- and under-dispersed data. The parameter estimation through the classical point of view has been done using the method of maximum likelihood, whereas, in the Bayesian framework, assuming independent beta priors of model parameters, the Metropolis–Hastings algorithm within Gibbs sampler is used to obtain sample-based Bayes estimates of the unknown parameters of the proposed model. A detailed simulation study is carried out to examine the outcomes of maximum likelihood and Bayesian estimators. Finally, two distinctive real data sets are analyzed using the proposed model. These applications showed the flexibility of the new distribution. Full article
(This article belongs to the Special Issue Recent Advances in Statistical Modeling and Simulations with Applications)
►▼ Show Figures

Figure 1

12 pages, 5575 KiB  
Article
Hidden Dynamics and Hybrid Synchronization of Fractional-Order Memristive Systems
by Haipeng Jiang, Lizhou Zhuang, Cheng Chen and Zuolei Wang
Axioms 2022, 11(11), 645; https://doi.org/10.3390/axioms11110645 - 15 Nov 2022
Cited by 1 | Viewed by 1108
Abstract
A fractional-order memristive system without equilibrium is addressed. Hidden attractors in the proposed system are discussed and the coexistence of a hidden attractor is found. Via theoretical analysis, the hybrid synchronization of the proposed system with partial controllers is investigated using fractional stability [...] Read more.
A fractional-order memristive system without equilibrium is addressed. Hidden attractors in the proposed system are discussed and the coexistence of a hidden attractor is found. Via theoretical analysis, the hybrid synchronization of the proposed system with partial controllers is investigated using fractional stability theory. Numerical simulation verifies the validity of the hybrid synchronization scheme. Full article
(This article belongs to the Special Issue Fractional-Order Equations and Optimization Models in Engineering)
►▼ Show Figures

Figure 1

13 pages, 297 KiB  
Article
On Some New Dynamic Inequalities Involving C-Monotonic Functions on Time Scales
by Ghada AlNemer, A. I. Saied, A. M. Hassan, Clemente Cesarano, Haytham M. Rezk and Mohammed Zakarya
Axioms 2022, 11(11), 644; https://doi.org/10.3390/axioms11110644 - 15 Nov 2022
Cited by 3 | Viewed by 1081
Abstract
In this paper, we establish some new dynamic inequalities involving C-monotonic functions with C≥1, on time scales. As a special case of our results when C=1, we obtain the inequalities involving increasing or decreasing functions (where [...] Read more.
In this paper, we establish some new dynamic inequalities involving C-monotonic functions with C≥1, on time scales. As a special case of our results when C=1, we obtain the inequalities involving increasing or decreasing functions (where for C=1, the 1-decreasing function is decreasing and the 1-increasing function is increasing). The main results are proved by applying the properties of C-monotonic functions and the chain rule formula on time scales. As a special case of our results, when T=R, we obtain refinements of some well-known continuous inequalities and when T=N, to the best of the authors’ knowledge, the results are essentially new. Full article
(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Analysis)
11 pages, 320 KiB  
Article
Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach
by Tibor K. Pogány
Axioms 2022, 11(11), 643; https://doi.org/10.3390/axioms11110643 - 14 Nov 2022
Viewed by 1188
Abstract
The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the case of a not exhaustively investigated non-homogeneous kernel, [...] Read more.
The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the case of a not exhaustively investigated non-homogeneous kernel, which mutually covers the homogeneous kernel cases as well. Particularly, novel Hilbert’s double series inequality results are presented, which include the upper bounds built exclusively with non-weighted ℓp–norms. The main mathematical tools are the integral expression of Mathieu (a,λ)-series, the Hölder inequality and a generalization of the double series theorem by Yang. Full article
(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications)
12 pages, 1020 KiB  
Article
Solving Time-Fractional Partial Differential Equation Using Chebyshev Cardinal Functions
by Haifa Bin Jebreen and Carlo Cattani
Axioms 2022, 11(11), 642; https://doi.org/10.3390/axioms11110642 - 14 Nov 2022
Cited by 1 | Viewed by 1675
Abstract
We propose a numerical scheme based on the Galerkin method for solving the time-fractional partial differential equations. To this end, after introducing the Chebyshev cardinal functions (CCFs), using the relation between fractional integral and derivative, we represent the Caputo fractional derivative based on [...] Read more.
We propose a numerical scheme based on the Galerkin method for solving the time-fractional partial differential equations. To this end, after introducing the Chebyshev cardinal functions (CCFs), using the relation between fractional integral and derivative, we represent the Caputo fractional derivative based on these bases and obtain an operational matrix. Applying the Galerkin method and using the operational matrix for the Caputo fractional derivative, the desired equation reduces to a system of linear algebraic equations. By solving this system, the unknown solution is obtained. The convergence analysis for this method is investigated, and some numerical simulations show the accuracy and ability of the technique. Full article
(This article belongs to the Special Issue Mathematical Modeling with Differential Equations)
►▼ Show Figures

Figure 1

15 pages, 305 KiB  
Article
On h-Quasi-Hemi-Slant Riemannian Maps
by Mohd Bilal, Sushil Kumar, Rajendra Prasad, Abdul Haseeb and Sumeet Kumar
Axioms 2022, 11(11), 641; https://doi.org/10.3390/axioms11110641 - 14 Nov 2022
Cited by 1 | Viewed by 1119
Abstract
In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability [...] Read more.
In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability of distributions, geometry of foliations, the condition for such maps to be totally geodesic, etc. At the end of this article, we give two non-trivial examples of this notion. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
20 pages, 1141 KiB  
Article
Optical Solitons in Fiber Bragg Gratings with Dispersive Reflectivity Having Five Nonlinear Forms of Refractive Index
by Ming-Yue Wang, Anjan Biswas, Yakup Yıldırım, Hashim M. Alshehri, Luminita Moraru and Simona Moldovanu
Axioms 2022, 11(11), 640; https://doi.org/10.3390/axioms11110640 - 13 Nov 2022
Cited by 7 | Viewed by 1225
Abstract
This paper implements the trial equation approach to retrieve cubic–quartic optical solitons in fiber Bragg gratings with the aid of the trial equation methodology. Five forms of nonlinear refractive index structures are considered. They are the Kerr law, the parabolic law, the polynomial [...] Read more.
This paper implements the trial equation approach to retrieve cubic–quartic optical solitons in fiber Bragg gratings with the aid of the trial equation methodology. Five forms of nonlinear refractive index structures are considered. They are the Kerr law, the parabolic law, the polynomial law, the quadratic–cubic law, and the parabolic nonlocal law. Dark and singular soliton solutions are recovered along with Jacobi’s elliptic functions with an appropriate modulus of ellipticity. Full article
(This article belongs to the Section Mathematical Analysis)
►▼ Show Figures

Figure 1

15 pages, 1025 KiB  
Article
Towards Optimal Robustness of Network Controllability by Nested-Edge Rectification
by Zhuoran Yu, Junfeng Nie and Junli Li
Axioms 2022, 11(11), 639; https://doi.org/10.3390/axioms11110639 - 13 Nov 2022
Cited by 1 | Viewed by 1224
Abstract
When a network is attacked, the network controllability decreases and the network is at risk of collapse. A network with good controllability robustness can better maintain its own controllability while under attack to provide time for network recovery. In order to explore how [...] Read more.
When a network is attacked, the network controllability decreases and the network is at risk of collapse. A network with good controllability robustness can better maintain its own controllability while under attack to provide time for network recovery. In order to explore how to build a network with optimal controllability robustness, an exhaustive search with adding edges was executed on a given set of small-sized networks. By exhaustive search, we mean: (1) All possible ways of adding edges, except self-loops, were considered and calculated at the time of adding each edge. (2) All possible node removal sequences were taken into account. The nested ring structure (NRS) was obtained from the result of the exhaustive search. NRS has a backbone ring, and the remaining edges of each node point to the nearest nodes along the direction of the backbone ring’s edges. The NRS satisfies an empirically necessary condition (ENC) and has great ability to resist random attacks. Therefore, nested edge rectifcation (NER) was designed to optimize the network for controllability robustness by constructing NRS in networks. NER was compared with the random edge rectification (RER) strategy and the unconstrained rewiring (UCR) strategy on synthetic networks and real-world networks by simulation. The simulation results show that NER can better improve the robustness of network’s controllability, and NER can also quickly improve the initial network controllability for networks with more than one driver node. In addition, as NER is executed, NRS gains more edges in the network, so the network has better controllability robustness. NER will be helpful for network model design or network optimization in future. Full article
(This article belongs to the Special Issue Complex Networks, Evolutionary Computation and Machine Learning)
►▼ Show Figures

Figure 1

12 pages, 11252 KiB  
Article
The Λ-Fractional Hydrocephalus Model
by Anastasios K. Lazopoulos, Dimitrios Karaoulanis and Kostantinos A. Lazopoulos
Axioms 2022, 11(11), 638; https://doi.org/10.3390/axioms11110638 - 12 Nov 2022
Viewed by 915
Abstract
Infant hydrocephalus is a clinically abnormal clinical state with an accumulation of fluid in cavities (ventricles) deep within the brain. Hence, pressure is increased inside the skull. The ventricles widen due to the excess fluid applying pressure upon the (parenchyma) brain tissues. The [...] Read more.
Infant hydrocephalus is a clinically abnormal clinical state with an accumulation of fluid in cavities (ventricles) deep within the brain. Hence, pressure is increased inside the skull. The ventricles widen due to the excess fluid applying pressure upon the (parenchyma) brain tissues. The infant brain tissue is described by a biomechanics model as a hyperelastic, Λ-fractional viscoelastic material, trying to describe the various conditions developing hydrocephalus. Λ-fractional continuum mechanics is applied with time variables due to viscosity and space fractional variables due to porosity. The simultaneous influence of both the viscosity and porosity of the membrane material (parenchyma) increases the cerebrospinal fluid’s pressure, causing the fluid’s accumulation in the brain. Full article
(This article belongs to the Section Mathematical Physics)
►▼ Show Figures

Figure 1

8 pages, 277 KiB  
Article
Analytic Approximate Solution in the Neighborhood of a Moving Singular Point of a Class of Nonlinear Equations
by Victor Orlov and Magomedyusuf Gasanov
Axioms 2022, 11(11), 637; https://doi.org/10.3390/axioms11110637 - 12 Nov 2022
Cited by 5 | Viewed by 1035
Abstract
The paper considers a class of nonlinear differential equations which are not solvable in quadratures in general case. The author’s technology for solving such equations contains six problems. In this article, the solution to one of these problems is given, a real area [...] Read more.
The paper considers a class of nonlinear differential equations which are not solvable in quadratures in general case. The author’s technology for solving such equations contains six problems. In this article, the solution to one of these problems is given, a real area in which it is possible to calculate an analytical approximate solution in the case of an approximate value of a moving singular point is obtained. Obtained results are based on the application of elements of differential calculus in finding estimates for the approximate solution error. Theoretical provisions are confirmed by numerical calculations, which characterize their reliability. Full article
(This article belongs to the Special Issue Mathematical Analysis Is the Theoretical Basis of a Number of Mathematical Disciplines)
17 pages, 433 KiB  
Article
Non-Canonical Functional Differential Equation of Fourth-Order: New Monotonic Properties and Their Applications in Oscillation Theory
by Amany Nabih, Clemente Cesarano, Osama Moaaz, Mona Anis and Elmetwally M. Elabbasy
Axioms 2022, 11(11), 636; https://doi.org/10.3390/axioms11110636 - 12 Nov 2022
Cited by 5 | Viewed by 1190
Abstract
In the present article, we iteratively deduce new monotonic properties of a class from the positive solutions of fourth-order delay differential equations. We discuss the non-canonical case in which there are possible decreasing positive solutions. Then, we find iterative criteria that exclude the [...] Read more.
In the present article, we iteratively deduce new monotonic properties of a class from the positive solutions of fourth-order delay differential equations. We discuss the non-canonical case in which there are possible decreasing positive solutions. Then, we find iterative criteria that exclude the existence of these positive decreasing solutions. Using these new criteria and based on the comparison and Riccati substitution methods, we create sufficient conditions to ensure that all solutions of the studied equation oscillate. In addition to having many applications in various scientific domains, the study of the oscillatory and non-oscillatory features of differential equation solutions is a theoretically rich field with many intriguing issues. Finally, we show the importance of the results by applying them to special cases of the studied equation. Full article
(This article belongs to the Special Issue Theory of Functions and Applications)
►▼ Show Figures

Figure 1

21 pages, 366 KiB  
Article
Strong Players and Stable Coalition Structures in PMAS Profit Game
by Ana Meca and Greys Sošić
Axioms 2022, 11(11), 635; https://doi.org/10.3390/axioms11110635 - 10 Nov 2022
Cited by 1 | Viewed by 1465
Abstract
In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a [...] Read more.
In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions. Full article
(This article belongs to the Special Issue Strategic Decision Models and Applications)
►▼ Show Figures

Figure 1

18 pages, 335 KiB  
Article
Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order
by Amar Benkerrouche, Mohammed Said Souid, Gani Stamov and Ivanka Stamova
Axioms 2022, 11(11), 634; https://doi.org/10.3390/axioms11110634 - 10 Nov 2022
Cited by 6 | Viewed by 1396
Abstract
In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established [...] Read more.
In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis of Fractional Chaotic Systems and Their Applications)
15 pages, 1606 KiB  
Article
Solving Biharmonic Equations with Tri-Cubic C1 Splines on Unstructured Hex Meshes
by Jeremy Youngquist and Jörg Peters
Axioms 2022, 11(11), 633; https://doi.org/10.3390/axioms11110633 - 10 Nov 2022
Cited by 1 | Viewed by 1493
Abstract
Unstructured hex meshes are partitions of three spaces into boxes that can include irregular edges, where n≠4 boxes meet along an edge, and irregular points, where the box arrangement is not consistent with a tensor-product grid. A new class of tri-cubic [...] Read more.
Unstructured hex meshes are partitions of three spaces into boxes that can include irregular edges, where n≠4 boxes meet along an edge, and irregular points, where the box arrangement is not consistent with a tensor-product grid. A new class of tri-cubic C1 splines is evaluated as a tool for solving elliptic higher-order partial differential equations over unstructured hex meshes. Convergence rates for four levels of refinement are computed for an implementation of the isogeometric Galerkin approach applied to Poisson’s equation and the biharmonic equation. The ratios of error are contrasted and superior to an implementation of Catmull-Clark solids. For the trivariate Poisson problem on irregularly partitioned domains, the reduction by 24 in the L2 norm is consistent with the optimal convergence on a regular grid, whereas the convergence rate for Catmull-Clark solids is measured as O(h3). The tri-cubic splines in the isogeometric framework correctly solve the trivariate biharmonic equation, but the convergence rate in the irregular case is lower than O(h4). An optimal reduction of 24 is observed when the functions on the C1 geometry are relaxed to be C0. Full article
(This article belongs to the Special Issue Higher Order Differential Equations)
►▼ Show Figures

Figure 1

18 pages, 1202 KiB  
Article
A Malware Propagation Model Considering Conformity Psychology in Social Networks
by Qingyi Zhu, Yuhang Liu, Xuhang Luo and Kefei Cheng
Axioms 2022, 11(11), 632; https://doi.org/10.3390/axioms11110632 - 10 Nov 2022
Cited by 1 | Viewed by 1704
Abstract
At present, malware is still a major security threat to computer networks. However, only a fraction of users with some security consciousness take security measures to protect computers on their own initiative, and others who know the current situation through social networks usually [...] Read more.
At present, malware is still a major security threat to computer networks. However, only a fraction of users with some security consciousness take security measures to protect computers on their own initiative, and others who know the current situation through social networks usually follow suit. This phenomenon is referred to as conformity psychology. It is obvious that more users will take countermeasures to prevent computers from being infected if the malware spreads to a certain extent. This paper proposes a deterministic nonlinear SEIQR propagation model to investigate the impact of conformity psychology on malware propagation. Both the local and global stabilities of malware-free equilibrium are proven while the existence and local stability of endemic equilibrium is proven by using the central manifold theory. Additionally, some numerical examples and simulation experiments based on two network datasets are performed to verify the theoretical analysis results. Finally, the sensitivity analysis of system parameters is carried out. Full article
(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
►▼ Show Figures

Figure 1

10 pages, 268 KiB  
Article
Some Inequalities for Certain p-Valent Functions Connected with the Combination Binomial Series and Confluent Hypergeometric Function
by Sheza M. El-Deeb and Adriana Cătaş
Axioms 2022, 11(11), 631; https://doi.org/10.3390/axioms11110631 - 10 Nov 2022
Cited by 2 | Viewed by 1030
Abstract
The present paper deals with a new differential operator denoted by Fp,tδ,n,b,c,m,β, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory [...] Read more.
The present paper deals with a new differential operator denoted by Fp,tδ,n,b,c,m,β, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory function. The new introduced operator is defined by making use of a linear combination of the binomial series and confluent hypergeometric function. In addition, by using special values of the parameters, we establish certain results concretized in specific corollaries, which provide useful inequalities. Studying these properties by using various types of operators is a technique that is widely used. Full article
(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)
13 pages, 297 KiB  
Article
Existence Results for an m-Point Mixed Fractional-Order Problem at Resonance on the Half-Line
by Ogbu F. Imaga, Samuel A. Iyase and Peter O. Ogunniyi
Axioms 2022, 11(11), 630; https://doi.org/10.3390/axioms11110630 - 09 Nov 2022
Cited by 3 | Viewed by 1169
Abstract
This work considers the existence of solutions for a mixed fractional-order boundary value problem at resonance on the half-line. The Mawhin’s coincidence degree theory will be used to prove existence results when the dimension of the kernel of the linear fractional differential operator [...] Read more.
This work considers the existence of solutions for a mixed fractional-order boundary value problem at resonance on the half-line. The Mawhin’s coincidence degree theory will be used to prove existence results when the dimension of the kernel of the linear fractional differential operator is equal to two. An example is given to demonstrate the main result obtained. Full article
(This article belongs to the Special Issue Recent Advances in Fractional Calculus)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-81
Previous Issue
Next Issue
Back to TopTop