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Symmetry
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New Trends on the Mathematical Models and Solitons Arising in...
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New Trends on the Mathematical Models and Solitons Arising in Real-World Problems

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 26689

Special Issue Editors

Prof. Dr. Haci Mehmet Baskonus

E-Mail Website
Guest Editor
Faculty of Education, Harran University, 63050 Sanliurfa, Turkey
Interests: applied science; partial differential equations; soliton theory; analytical methods; numerical methods
Special Issues, Collections and Topics in MDPI journals
Dr. Yolanda Guerrero

E-Mail Website
Guest Editor
Departamento de Anatomía y Psicobiología, Universidad de Murcia, 30001-Murcia, Spain
Interests: desease modeling

Special Issue Information

Dear Colleagues, 

The essence of mathematical tools for exemplifying the practical problems that exist in daily life is as old as the world itself. Mathematical models in science and technology have recently attracted an increased amount of researcher attentions with the aim to understand, describe, and predict the future behavior of natural phenomena. Recent studies on fractional calculus have been particularly popular among researchers due to their favorable properties when analyzing real-world models associated with properties such as anomalous diffusion, non-Markovian processes, random walk, long range, and most importantly heterogeneous behaviors. The concept of local differential operators along with power-law settings and non-local differential operators was suggested in order to accurately replicate the above-cited natural processes. The complexities of nature have led mathematicians and physicists to derive the most sophisticated and scientific mathematical operators to accurately replicate and capture pragmatic realities.

Mathematical physics plays a vital role in the study of the determinants and distribution of solitons. With the help of this, we can identify wave distributions in many fields of nonlinear sciences, and many experts have recently focused their work on this field. Further, these types of studies may help us to provide the foundation for developing public policy and make regulatory decisions relating to engineering problems, as well as to evaluate both existing and new perspectives. Major areas of mathematical physics studies with mathematical models include physics, symmetry, transmission, outbreak investigation, and epidemiological problems.

This particular issue is devoted to the collection of new results, extending from theory to practice, with the aim of developing new technological tools. This Special Issue will be focused on but not limited to:

Topics:

  • Theoretical, computational, and experimental nature of mathematical physics models;
  • Review performance of mathematical models with fractional differential and integral equations;
  • Evaluation of models with different types of fractional operators;
  • Validation of models with fractal–fractional differential and integral operators;
  • Review of effect of new fractal differential and integral operators for modeling, such as epidemiological diseases, mathematical physics, soliton theory, and so on.

Submit your paper and select the Journal “Symmetry” and the Special Issue “New Trends on the Mathematical Models and Solitons Arising in Real-World Problems such as Engineering, Physics, Health, and Epidemiological Diseases” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Dr. Haci Mehmet Baskonus
Dr. Yolanda Guerrero
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical physics
  • partial differential equations
  • epidemic models
  • basic reproduction number
  • fractional differential equations
  • dynamical systems
  • stability analysis
  • bifurcation
  • optimal control

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Published Papers (16 papers)

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Editorial

Jump to: Research

6 pages, 197 KiB  
Editorial
New Trends on the Mathematical Models and Solitons Arising in Real-World Problems
by Haci Mehmet Baskonus
Symmetry 2024, 16(1), 1; https://doi.org/10.3390/sym16010001 - 19 Dec 2023
Viewed by 751
Abstract
The essence of mathematical tools used to exemplify the practical problems that exist in daily life is as old as the world itself [...] Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)

Research

Jump to: Editorial

27 pages, 383 KiB  
Article
Analysis of Implicit Solutions for a Coupled System of Hybrid Fractional Order Differential Equations with Hybrid Integral Boundary Conditions in Banach Algebras
by Yahia Awad and Yousuf Alkhezi
Symmetry 2023, 15(9), 1758; https://doi.org/10.3390/sym15091758 - 13 Sep 2023
Cited by 3 | Viewed by 584
Abstract
This paper investigates the existence and uniqueness of implicit solutions in a coupled symmetry system of hybrid fractional order differential equations, along with hybrid integral boundary conditions in Banach Algebras. The methodology centers on a hybrid fixed-point theorem that involves mixed Lipschitz and [...] Read more.
This paper investigates the existence and uniqueness of implicit solutions in a coupled symmetry system of hybrid fractional order differential equations, along with hybrid integral boundary conditions in Banach Algebras. The methodology centers on a hybrid fixed-point theorem that involves mixed Lipschitz and Carathéodory conditions, serving to establish the existence of solutions. Moreover, it derives sufficient conditions for solution uniqueness and establishes the Hyers–Ulam types of solution stability. This study contributes valuable insights into complex hybrid fractional order systems and their practical implications. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
13 pages, 711 KiB  
Article
Application of Fractional SIQRV Model for SARS-CoV-2 and Stability Analysis
by Zafer Öztürk, Halis Bilgil and Sezer Sorgun
Symmetry 2023, 15(5), 1048; https://doi.org/10.3390/sym15051048 - 09 May 2023
Cited by 2 | Viewed by 986
Abstract
Throughout history, infectious diseases have been the cause of outbreaks and the deaths of people. It is crucial for endemic disease management to be able to forecast the number of infections at a given moment and the frequency of new infections so that [...] Read more.
Throughout history, infectious diseases have been the cause of outbreaks and the deaths of people. It is crucial for endemic disease management to be able to forecast the number of infections at a given moment and the frequency of new infections so that the appropriate precautions can be taken. The COVID-19 pandemic has highlighted the value of mathematical modeling of pandemics. The susceptible–infected–quarantined–recovered–vaccinated (SIQRV) epidemic model was used in this work. Symmetrical aspects of the proposed dynamic model, disease-free equilibrium, and stability were analyzed. The symmetry of the population size over time allows the model to find stable equilibrium points for any parameter value and initial conditions. The assumption of the strong symmetry of the initial conditions and parameter values plays a key role in the analysis of the fractional SIQRV model. In order to combat the pandemic nature of the disease, control the disease in the population, and increase the possibility of eradicating the disease, effective control measures include quarantine and immunization. Fractional derivatives are used in the Caputo sense. In the model, vaccination and quarantine are two important applications for managing the spread of the pandemic. Although some of the individuals who were vaccinated with the same type and equal dose of vaccine gained strong immunity thanks to the vaccine, the vaccine could not give sufficient immunity to the other part of the population. This is thought to be related the structural characteristics of individuals. Thus, although some of the individuals vaccinated with the same strategy are protected against the virus for a long time, others may become infected soon after vaccination. Appropriate parameters were used in the model to reflect this situation. In order to validate the model, the model was run by taking the COVID-19 data of Türkiye about a year ago, and the official data on the date of this study were successfully obtained. In addition to the stability analysis of the model, numerical solutions were obtained using the fractional Euler method. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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9 pages, 277 KiB  
Article
Processing Fractional Differential Equations Using ψ-Caputo Derivative
by Mahrouz Tayeb, Hamid Boulares, Abdelkader Moumen and Moheddine Imsatfia
Symmetry 2023, 15(4), 955; https://doi.org/10.3390/sym15040955 - 21 Apr 2023
Cited by 3 | Viewed by 1150
Abstract
Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness of solutions (EUS) for FDEs in [...] Read more.
Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness of solutions (EUS) for FDEs in the sense ψ-Caputo fractional derivative (ψ-CFD) in the second-order 1<α<2. We know that ψ-CFD is a generalization of previously familiar fractional derivatives: Riemann-Liouville and Caputo. By applying the Banach fixed-point theorem (BFPT) and the Schauder fixed-point theorem (SFPT), we obtained the desired results, and to embody the theoretical results obtained, we provided two examples that illustrate the theoretical proofs. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
24 pages, 930 KiB  
Article
Statistical Inference of the Half Logistic Modified Kies Exponential Model with Modeling to Engineering Data
by Safar M. Alghamdi, Mansour Shrahili, Amal S. Hassan, Ahmed M. Gemeay, Ibrahim Elbatal and Mohammed Elgarhy
Symmetry 2023, 15(3), 586; https://doi.org/10.3390/sym15030586 - 23 Feb 2023
Cited by 10 | Viewed by 3545
Abstract
The half-logistic modified Kies exponential (HLMKEx) distribution is a novel three-parameter model that is introduced in the current work to expand the modified Kies exponential distribution and improve its flexibility in modeling real-world data. Due to its versatility, the density function of the [...] Read more.
The half-logistic modified Kies exponential (HLMKEx) distribution is a novel three-parameter model that is introduced in the current work to expand the modified Kies exponential distribution and improve its flexibility in modeling real-world data. Due to its versatility, the density function of the HLMKEx distribution offers symmetrical, asymmetrical, unimodal, and reversed-J-shaped, as well as increasing, reversed-J shaped, and upside-down hazard rate forms. An infinite linear representation can be used to represent the HLMKEx density. The HLMKEx model’s fundamental mathematical features are obtained, such as the quantile function, moments, incomplete moments, and moments of residuals. Additionally, some measures of uncertainty as well as stochastic ordering are derived. To estimate its parameters, eight estimation methods are used. With the use of detailed simulation data, we compare the performance of each estimating technique and obtain partial and total ranks for the accuracy measures of absolute bias, mean squared error, and mean absolute relative error. The simulation results demonstrate that, in contrast to other competing distributions, the proposed distribution can actually fit the data more accurately. Two actual data sets are investigated in the field of engineering to demonstrate the adaptability and application of the suggested distribution. The findings demonstrate that, in contrast to other competing distributions, the provided distribution can actually fit the data more accurately. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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12 pages, 1519 KiB  
Article
Effects of M-Truncated Derivative and Multiplicative Noise on the Exact Solutions of the Breaking Soliton Equation
by Wael W. Mohammed, M. El-Morshedy, Abdelkader Moumen, Ekram E. Ali, M. Benaissa and Ahmed E. Abouelregal
Symmetry 2023, 15(2), 288; https://doi.org/10.3390/sym15020288 - 20 Jan 2023
Cited by 9 | Viewed by 1236
Abstract
In this article, the fractional–space stochastic (2+1)-dimensional breaking soliton equation (SFSBSE) is taken into account in the sense of M-Truncated derivative. To get the exact solutions to the SFSBSE, we use the modified F-expansion method. There are several varieties of obtained exact solutions, [...] Read more.
In this article, the fractional–space stochastic (2+1)-dimensional breaking soliton equation (SFSBSE) is taken into account in the sense of M-Truncated derivative. To get the exact solutions to the SFSBSE, we use the modified F-expansion method. There are several varieties of obtained exact solutions, including trigonometric and hyperbolic functions. The attained solutions of the SFSBSE established in this paper extend a number of previously attained results. Moreover, in order to clarify the influence of multiplicative noise and M-Truncated derivative on the behavior and symmetry of the solutions for the SFSBSE, we employ Matlab to plot three-dimensional and two-dimensional diagrams of the exact fractional–stochastic solutions achieved here. In general, a noise term that destroy the symmetry of the solutions increases the solution’s stability. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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18 pages, 1993 KiB  
Article
Numerical Solution of Time-Fractional Emden–Fowler-Type Equations Using the Rational Homotopy Perturbation Method
by Kholoud Saad Albalawi, Badr Saad Alkahtani, Ashish Kumar and Pranay Goswami
Symmetry 2023, 15(2), 258; https://doi.org/10.3390/sym15020258 - 17 Jan 2023
Cited by 5 | Viewed by 1202
Abstract
The integral-order derivative is not suitable where infinite variances are expected, and the fractional derivative manages to consider effects with more precision; therefore, we considered timefractional Emden–Fowler-type equations and solved them using the rational homotopy perturbation method (RHPM). The RHPM method is based [...] Read more.
The integral-order derivative is not suitable where infinite variances are expected, and the fractional derivative manages to consider effects with more precision; therefore, we considered timefractional Emden–Fowler-type equations and solved them using the rational homotopy perturbation method (RHPM). The RHPM method is based on two power series in rational form. The existence and uniqueness of the equation are proved using the Banach fixed-point theorem. Furthermore, we approximate the term h(z) with a polynomial of a suitable degree and then solve the system using the proposed method and obtain an approximate symmetric solution. Two numerical examples are investigated using this proposed approach. The effectiveness of the proposed approach is checked by representing the graphs of exact and approximate solutions. The table of absolute error is also presented to understand the method′s accuracy. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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22 pages, 1071 KiB  
Article
Construction of Solitary Wave Solutions to the (3 + 1)-Dimensional Nonlinear Extended and Modified Quantum Zakharov–Kuznetsov Equations Arising in Quantum Plasma Physics
by Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Abdulrahman F. AlJohani, Weam Alharbi and Amal F. Alharbi
Symmetry 2023, 15(1), 248; https://doi.org/10.3390/sym15010248 - 16 Jan 2023
Cited by 8 | Viewed by 1702
Abstract
Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and [...] Read more.
Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The derived results via the MEAEM method, ESE method, and modified F-expansion have been retrieved and will be expedient in the future to illuminate the collaboration between lower nonlinear ion-acoustic waves. For the physical behavior of the models, some solutions are plotted graphically in 2D and 3D by imparting particular values to the parameters under the given condition at each solution. Hence explored solutions have profitable rewards in the field of mathematical physics. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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27 pages, 4345 KiB  
Article
A Fractional Atmospheric Circulation System under the Influence of a Sliding Mode Controller
by Ramapura N. Premakumari, Chandrali Baishya, Pundikala Veeresha and Lanre Akinyemi
Symmetry 2022, 14(12), 2618; https://doi.org/10.3390/sym14122618 - 10 Dec 2022
Cited by 19 | Viewed by 1327
Abstract
The earth’s surface is heated by the large-scale movement of air known as atmospheric circulation, which works in conjunction with ocean circulation. More than 105 variables are involved in the complexity of the weather system. In this work, we analyze the dynamical [...] Read more.
The earth’s surface is heated by the large-scale movement of air known as atmospheric circulation, which works in conjunction with ocean circulation. More than 105 variables are involved in the complexity of the weather system. In this work, we analyze the dynamical behavior and chaos control of an atmospheric circulation model known as the Hadley circulation model, in the frame of Caputo and Caputo–Fabrizio fractional derivatives. The fundamental novelty of this paper is the application of the Caputo derivative with equal dimensionality to models that includes memory. A sliding mode controller (SMC) is developed to control chaos in this fractional-order atmospheric circulation system with uncertain dynamics. The proposed controller is applied to both commensurate and non-commensurate fractional-order systems. To demonstrate the intricacy of the models, we plot some graphs of various fractional orders with appropriate parameter values. We have observed the influence of thermal forcing on the dynamics of the system. The outcome of the analytical exercises is validated using numerical simulations. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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15 pages, 1029 KiB  
Article
Diverse Variety of Exact Solutions for Nonlinear Gilson–Pickering Equation
by Seham Ayesh Allahyani, Hamood Ur Rehman, Aziz Ullah Awan, ElSayed M. Tag-ElDin and Mahmood Ul Hassan
Symmetry 2022, 14(10), 2151; https://doi.org/10.3390/sym14102151 - 14 Oct 2022
Cited by 15 | Viewed by 1292
Abstract
The purpose of this article is to achieve new soliton solutions of the Gilson–Pickering equation (GPE) with the assistance of Sardar’s subequation method (SSM) and Jacobi elliptic function method (JEFM). The applications of the GPE is wider because we study some valuable and [...] Read more.
The purpose of this article is to achieve new soliton solutions of the Gilson–Pickering equation (GPE) with the assistance of Sardar’s subequation method (SSM) and Jacobi elliptic function method (JEFM). The applications of the GPE is wider because we study some valuable and vital equations such as Fornberg–Whitham equation (FWE), Rosenau–Hyman equation (RHE) and Fuchssteiner–Fokas–Camassa–Holm equation (FFCHE) obtained by particular choices of parameters involved in the GPE. Many techniques are available to convert PDEs into ODEs for extracting wave solutions. Most of these techniques are a case of symmetry reduction, known as nonclassical symmetry. In our work, this approach is used to convert a PDE to an ODE and obtain the exact solutions of the NLPDE. The solutions obtained are unique, remarkable, and significant for readers. Mathematica 11 software is used to derive the solutions of the presented model. Moreover, the diagrams of the acquired solutions for distinct values of parameters were demonstrated in two and three dimensions along with contour plots. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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21 pages, 4325 KiB  
Article
Study of Transmission Dynamics of Streptococcus suis Infection Mathematical Model between Pig and Human under ABC Fractional Order Derivative
by Din Prathumwan, Inthira Chaiya and Kamonchat Trachoo
Symmetry 2022, 14(10), 2112; https://doi.org/10.3390/sym14102112 - 11 Oct 2022
Cited by 2 | Viewed by 1309
Abstract
In this paper, a mathematical model for Streptococcus suis infection is improved by using the fractional order derivative. The modified model also investigates the transmission between pigs and humans. The proposed model can classify the pig population density into four classes, which are [...] Read more.
In this paper, a mathematical model for Streptococcus suis infection is improved by using the fractional order derivative. The modified model also investigates the transmission between pigs and humans. The proposed model can classify the pig population density into four classes, which are pig susceptible class, pig infectious class, pig quarantine class, and pig recovery class. Moreover, the human population density has been separated into three classes, these are human susceptible class, human infectious class, and human recovery class. The spread of the infection is analyzed by considering the contact between humans and pigs. The basic reproduction number (R0), the infectious indicator, is carried out using the next generation matrix. The disease-free equilibrium is locally asymptotically stable if R0<1, and the endemic equilibrium is locally asymptotically stable if R0>1. The theoretical analyses of the fractional order derivative model, existence and uniqueness, have been proposed. The numerical examples were illustrated to support the proposed stability theorems. The results show that the fractional order derivative model provides the various possible solution trajectories with different fractional orders for the same parameters. In addition, transmission between pigs and humans resulted in the spread of Streptococcus suis infection. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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19 pages, 4122 KiB  
Article
Soliton Solutions and Sensitive Analysis of Modified Equal-Width Equation Using Fractional Operators
by Muhammad Bilal Riaz, Adam Wojciechowski, Georgia Irina Oros and Riaz Ur Rahman
Symmetry 2022, 14(8), 1731; https://doi.org/10.3390/sym14081731 - 19 Aug 2022
Cited by 9 | Viewed by 1491
Abstract
In this manuscript, the novel auxiliary equation methodology (NAEM) is employed to scrutinize various forms of solitary wave solutions for the modified equal-width wave (MEW) equation. M-truncated along with Atangana–Baleanu (AB)-fractional derivatives are employed to study the soliton [...] Read more.
In this manuscript, the novel auxiliary equation methodology (NAEM) is employed to scrutinize various forms of solitary wave solutions for the modified equal-width wave (MEW) equation. M-truncated along with Atangana–Baleanu (AB)-fractional derivatives are employed to study the soliton solutions of the problem. The fractional MEW equations are important for describing hydro-magnetic waves in cold plasma. A comparative analysis is utilized to study the influence of the fractional parameter on the generated solutions. Secured solutions include bright, dark, singular, periodic and many other types of soliton solutions. In compared to other methods, the solutions demonstrate that the proposed technique is particularly effective, straightforward, and trustworthy that contains families of solutions. In addition, the symbolic soft computation is used to verify the obtained solutions. Finally, the system is subjected to a sensitive analysis. Integer-order results calculated by the symmetry method present in the literature can be addressed as limiting cases of the present study. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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15 pages, 2158 KiB  
Article
Numerical Modeling and Symmetry Analysis of a Pine Wilt Disease Model Using the Mittag–Leffler Kernel
by V. Padmavathi, N. Magesh, K. Alagesan, M. Ijaz Khan, Samia Elattar, Mamdooh Alwetaishi and Ahmed M. Galal
Symmetry 2022, 14(5), 1067; https://doi.org/10.3390/sym14051067 - 23 May 2022
Cited by 7 | Viewed by 1554
Abstract
The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, [...] Read more.
The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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25 pages, 15640 KiB  
Article
Speed Regulation of a Permanent Magnet DC Motor with Sliding Mode Control Based on Washout Filter
by Hugo Velasco-Muñoz, John E. Candelo-Becerra, Fredy E. Hoyos and Alejandro Rincón
Symmetry 2022, 14(4), 728; https://doi.org/10.3390/sym14040728 - 03 Apr 2022
Cited by 4 | Viewed by 2121
Abstract
The accuracy of control systems applied to motors is influenced by uncertainties and abrupt variations of the load and system parameters. Some robust control strategies have been proposed in the literature for responding to disturbances and uncertainties, parametric variations, and non-linearities, adding complex [...] Read more.
The accuracy of control systems applied to motors is influenced by uncertainties and abrupt variations of the load and system parameters. Some robust control strategies have been proposed in the literature for responding to disturbances and uncertainties, parametric variations, and non-linearities, adding complex control rules and considerable computational efforts. Therefore, this paper presents the application of a sliding mode control method based on a washout filter (SMC-w) for speed control in a permanent magnet DC motor. In addition, the dynamic behavior of the SMC-w is evaluated under changes in the reference speed and load torque. The response of the control system under variations of the speed reference signal and load torque were studied. The results were contrasted with conventional proportional integral derivative (PID) control to evaluate the efficiency and improvement of the SMC-w. The qualitative shape of the transient response of the speed and current concerning changes in the reference speed is symmetric for the SMC-w controller, but the values of overshoot, settling time, and steady-state error are different. This technique has a great potential for industrial application as it controls efficiently with low computational cost and a simple design, which benefits its implementation in practical environments. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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15 pages, 9467 KiB  
Article
Numerical Validation of a Boost Converter Controlled by a Quasi-Sliding Mode Control Technique with Bifurcation Diagrams
by Simeón Casanova Trujillo, John E. Candelo-Becerra and Fredy E. Hoyos
Symmetry 2022, 14(4), 694; https://doi.org/10.3390/sym14040694 - 28 Mar 2022
Cited by 6 | Viewed by 1684
Abstract
A boost converter is an electronic circuit that generates a higher voltage in the output than in the input. The most common method to regulate the DC/DC converter is pulse-width modulation (PWM), and some techniques such as sliding mode control help perform a [...] Read more.
A boost converter is an electronic circuit that generates a higher voltage in the output than in the input. The most common method to regulate the DC/DC converter is pulse-width modulation (PWM), and some techniques such as sliding mode control help perform a switching frequency to determine the duty cycle. However, some instabilities at different operating points have been detected with the controllers that have not yet been studied. Therefore, this paper presents a numerical validation of the boost converter with bifurcation diagrams. The pulse-width modulation is controlled by using a quasi-sliding mode control technique, such as the zero average dynamics, because it allows for the reduction of some phenomena such as chattering, ripple, and distortions. The results show that N−T periodic orbits are detected with this technique from an initial operating point and they present a qualitative symmetry in both voltage and current variables. This technique is helpful to study a whole range of instability problems resulting from the different power converters and the controllers. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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17 pages, 2739 KiB  
Article
Numerical Solutions of the Mathematical Models on the Digestive System and COVID-19 Pandemic by Hermite Wavelet Technique
by Kumbinarasaiah Srinivasa, Haci Mehmet Baskonus and Yolanda Guerrero Sánchez
Symmetry 2021, 13(12), 2428; https://doi.org/10.3390/sym13122428 - 15 Dec 2021
Cited by 25 | Viewed by 2365
Abstract
This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system [...] Read more.
This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system by considering different parameters such as sleep factor, tension, food rate, death rate, and medicine. Here, we discussed how these parameters influence the digestive system and showed them through figures and tables. Another fractional model is used on the COVID-19 pandemic. This model is defined by a system of fractional-ODEs including five variables, called S (susceptible), E (exposed), I (infected), Q (quarantined), and R (recovered). The proposed wavelet technique investigates these two models. Here, we express the modeled equation in terms of the Hermite wavelets along with the collocation scheme. Then, using the properties of wavelets, we convert the modeled equation into a system of algebraic equations. We use the Newton–Raphson method to solve these nonlinear algebraic equations. The obtained results are compared with numerical solutions and the Runge–Kutta method (R–K method), which is expressed through tables and graphs. The HWM computational time (consumes less time) is better than that of the R–K method. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)
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