Submit to Mathematics Review for Mathematics Propose a Special Issue

Journal Menu

Journal Browser

Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Published Papers

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (15 May 2023) | Viewed by 21631

Share This Special Issue

Special Issue Editors

Dr. Calogero Vetro

E-Mail Website
Guest Editor

Associate Professor, Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
Interests: difference equations; flow invariance; nonlinear regularity theory; ordinary differential equations; partial differential equations; reduction methods; symmetry operators; weak symmetries
Special Issues, Collections and Topics in MDPI journals

Dr. Omar Bazighifan

E-Mail Website
Guest Editor

1. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
2. Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
Interests: qualitative theory; ordinary differential equations; functional differential equations; dynamical systems; mathematical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential equations, both partial (PDE) and ordinary (ODE), give key tools in understanding the mechanisms of physical systems and solving various problems of nonlinear phenomena. In particular, we mention diffusive processes, such as in problems in elasticity theory and in the study of porous media.

Abstract inequalities and functional equations are recognized as basic ingredients to carry out pure mathematics research (for example, in mathematical analysis and differential geometry) and applied mathematics research (for example, in mathematical physics and numerical analysis).

The above main fields are strongly related to each other. Indeed, the qualitative study of differential equations provides the appropriate framework setting to develop new inequalities and to consider different types of equations. On the other hand, these inequalities and equations are used to obtain useful estimates and bounds of terms in specific differential equations but also in characterizing the solutions' set.

There is a large and very active community of scientists working on these topics and focusing on their applications in dynamical programming, biology, information theory, statistics, physics, and engineering processes.

This Special Issue will collect ideas and significant contributions to the theories and applications of analytic inequalities, functional equations and differential equations. We welcome both original research articles and articles discussing the current state of the art.

Dr. Calogero Vetro
Dr. Omar Bazighifan
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

Functional, differential and difference inequalities
Functional and difference equations
ODE
PDE
Calculus of variations
Dynamical systems
Asymptotic analysis
Potential theory
Reduction and linearization techniques
Comparison methods
Differential models in engineering and physical sciences

Published Papers (16 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

12 pages, 274 KiB

Open AccessArticle

Weighted Hardy–Rellich Inequality for Dunkl Operators

by Jielin Lyu, Yongyang Jin, Shoufeng Shen and Li Tang

Mathematics 2023, 11(6), 1487; https://doi.org/10.3390/math11061487 - 18 Mar 2023

Viewed by 818

Abstract

In this paper, we proved a weighted Hardy–Rellich inequality for Dunkl operators based on the spherical h-harmonic decomposition theory of Dunkl operators. Moreover, we obtained the explicit constant of the inequalities, which is optimal in some cases. Our results extend some known inequalities. [...] Read more.

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

13 pages, 296 KiB

Open AccessArticle

Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized (E, h)-Convexity

by Wedad Saleh, Abdelghani Lakhdari, Ohud Almutairi and Adem Kiliçman

Mathematics 2023, 11(6), 1373; https://doi.org/10.3390/math11061373 - 12 Mar 2023

Cited by 4 | Viewed by 790

Abstract

In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite–Hadamard-type inequality using generalized

(E, h)

-convexity and obtain two identities pertaining to these operators, [...] Read more.

(E, h)

-convexity and obtain two identities pertaining to these operators, and the respective first- and second-order derivatives are given. In terms of applications, we provide some new generalized trapezoid-type inequalities for generalized (

E, h

)-convex functions. Finally, some special cases are deduced for different values of

δ

, E, and h. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

16 pages, 338 KiB

Open AccessArticle

New Results Concerning Approximate Controllability of Conformable Fractional Noninstantaneous Impulsive Stochastic Evolution Equations via Poisson Jumps

by Yazid Alhojilan and Hamdy M. Ahmed

Mathematics 2023, 11(5), 1093; https://doi.org/10.3390/math11051093 - 22 Feb 2023

Cited by 1 | Viewed by 922

Abstract

We introduce the conformable fractional (CF) noninstantaneous impulsive stochastic evolution equations with fractional Brownian motion (fBm) and Poisson jumps. The approximate controllability for the considered problem was investigated. Principles and concepts from fractional calculus, stochastic analysis, and the fixed-point theorem were used to [...] Read more.

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

16 pages, 348 KiB

Open AccessArticle

Fixed Points on Covariant and Contravariant Maps with an Application

by Rajagopalan Ramaswamy, Gunaseelan Mani, Arul Joseph Gnanaprakasam, Ola A. Ashour Abdelnaby, Vuk Stojiljković, Slobodan Radojevic and Stojan Radenović

Mathematics 2022, 10(22), 4385; https://doi.org/10.3390/math10224385 - 21 Nov 2022

Cited by 7 | Viewed by 1208

Abstract

Fixed-point results on covariant maps and contravariant maps in a

C^{★}

Fixed-point results on covariant maps and contravariant maps in a

C^{★}

-algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We have also provided an application to find an analytical solution to the integral equation and the electrical circuit differential equation. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

► Show Figures

Figure 1

22 pages, 379 KiB

Open AccessArticle

Regularity for Quasi-Linear p-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group

by Chengwei Yu

Mathematics 2022, 10(21), 4129; https://doi.org/10.3390/math10214129 - 05 Nov 2022

Cited by 1 | Viewed by 902

Abstract

When

2 - 1 / Q < p \leq 2

, we establish the

C_{loc}^{0, 1}

and

C_{loc}^{1, α}

-regularities of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in the Heisenberg group

H^{n}

, [...] Read more.

When

2 - 1 / Q < p \leq 2

, we establish the

C_{loc}^{0, 1}

and

C_{loc}^{1, α}

-regularities of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in the Heisenberg group

H^{n}

, where

Q = 2 n + 2

is the homogeneous dimension of

H^{n}

. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

15 pages, 4088 KiB

Open AccessArticle

Stochastic Analysis of a Hantavirus Infection Model

by Yousef Alnafisah and Moustafa El-Shahed

Mathematics 2022, 10(20), 3756; https://doi.org/10.3390/math10203756 - 12 Oct 2022

Viewed by 1080

Abstract

In this paper, a stochastic Hantavirus infection model is constructed. The existence, uniqueness, and boundedness of the positive solution of the stochastic Hantavirus infection model are derived. The conditions for the extinction of the Hantavirus infection from the stochastic system are obtained. Furthermore, the criteria for the presence of a unique ergodic stationary distribution for the Hantavirus infection model are established using a suitable Lyapunov function. Finally, the importance of environmental noise in the Hantavirus infection model is illustrated using the Milstein method. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

► Show Figures

Figure 1

49 pages, 540 KiB

Open AccessArticle

On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations

by Mawia Osman, Yonghui Xia, Omer Abdalrhman Omer and Ahmed Hamoud

Mathematics 2022, 10(13), 2295; https://doi.org/10.3390/math10132295 - 30 Jun 2022

Cited by 10 | Viewed by 1693

Abstract

In this article, we present the fuzzy Adomian decomposition method (ADM) and fuzzy modified Laplace decomposition method (MLDM) to obtain the solutions of fuzzy fractional Navier–Stokes equations in a tube under fuzzy fractional derivatives. We have looked at the turbulent flow of a viscous fluid in a tube, where the velocity field is a function of only one spatial coordinate, in addition to time being one of the dependent variables. Furthermore, we investigate the fuzzy Elzaki transform, and the fuzzy Elzaki decomposition method (EDM) applied to solving fuzzy linear-nonlinear Schrodinger differential equations. The proposed method worked perfectly without any need for linearization or discretization. Finally, we compared the fuzzy reduced differential transform method (RDTM) and fuzzy homotopy perturbation method (HPM) to solving fuzzy heat-like and wave-like equations with variable coefficients. The RDTM and HPM solutions are simpler than other already existing methods. Several examples are provided to illustrate the methods that have been offered. The results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. These studies are important in the context of the development of the theory of fuzzy partial differential equations. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

► Show Figures

Figure 1

8 pages, 270 KiB

Open AccessArticle

Existence of the Limit of Ratios of Consecutive Terms for a Class of Linear Recurrences

by Renato Fiorenza

Mathematics 2022, 10(12), 2065; https://doi.org/10.3390/math10122065 - 15 Jun 2022

Viewed by 1681

Abstract

Let

{(F_{n})}_{n = 1}^{\infty}

be the classical Fibonacci sequence. It is well known that the

lim F_{n + 1} / F_{n}

exists and equals the Golden Mean. If, more generally, [...] Read more.

Let

{(F_{n})}_{n = 1}^{\infty}

be the classical Fibonacci sequence. It is well known that the

lim F_{n + 1} / F_{n}

exists and equals the Golden Mean. If, more generally,

{(F_{n})}_{n = 1}^{\infty}

is an order-k linear recurrence with real constant coefficients, i.e.,

F_{n} = \sum_{j = 1}^{k} λ_{k + 1 - j} F_{n - j}

with

n > k

λ_{j} \in R

j = 1, \dots, k

, then the existence of the limit of ratios of consecutive terms may fail. In this paper, we show that the limit exists if the first k elements

F_{1}, F_{2}, \dots, F_{k}

{(F_{n})}_{n = 1}^{\infty}

are positive,

λ_{1}, \dots, λ_{k - 1}

are all nonnegative, at least one being positive, and

max (λ_{1}, \dots, λ_{k}) = λ_{k} \geq k

. The limit is characterized as fixed point, bounded below by

λ_{k}

and bounded above by

λ_{1} + λ_{2} + \dots + λ_{k}

. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

12 pages, 302 KiB

Open AccessArticle

Existence and Multiplicity of Solutions for a Bi-Non-Local Problem

by Jiabin Zuo, Tianqing An, Alessio Fiscella and Chungen Liu

Mathematics 2022, 10(12), 1973; https://doi.org/10.3390/math10121973 - 08 Jun 2022

Cited by 1 | Viewed by 1489

Abstract

The aim of this paper is to investigate the existence and multiplicity of solutions for a bi-non-local problem. Precisely, we show that the above problem admits at least a non-trivial positive energy solution by using the mountain pass theorem. Furthermore, with the help of the fountain theorem, we obtain the existence of infinitely many positive energy solutions, assuming a symmetric condition for g. The main feature and difficulty of this paper is the presence of a double non-local term involving two variable parameters. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

14 pages, 302 KiB

Open AccessArticle

Remarks on Nonlocal Dirichlet Problems

by Kholoud Saad Albalawi, Mona Bin-Asfour and Francesca Vetro

Mathematics 2022, 10(9), 1546; https://doi.org/10.3390/math10091546 - 04 May 2022

Viewed by 1153

Abstract

We study a nonlocal Dirichlet problem with the

(p (b (u)), q (b (u)))

-Laplacian operator and integrable data on a bounded domain with smooth boundary. We establish the existence of at [...] Read more.

We study a nonlocal Dirichlet problem with the

(p (b (u)), q (b (u)))

-Laplacian operator and integrable data on a bounded domain with smooth boundary. We establish the existence of at least one weak solution in the case the variable exponents of the leading operator depend on the solution u, without assuming any growth conditions on g. The proof is based on the characterization of the energy functional associated to the problem, using the methods of the calculus of variations. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

16 pages, 323 KiB

Open AccessArticle

The Existence and Multiplicity of Homoclinic Solutions for a Fractional Discrete p−Laplacian Equation

by Yong Wu, Bouali Tahar, Guefaifia Rafik, Abita Rahmoune and Libo Yang

Mathematics 2022, 10(9), 1400; https://doi.org/10.3390/math10091400 - 22 Apr 2022

Cited by 3 | Viewed by 1136

Abstract

In this study, we investigate the existence and multiplicity of solutions for a fractional discrete p−Laplacian equation on

Z

. Under suitable hypotheses on the potential function V and the nonlinearity f, with the aid of Ekeland’s variational principle, via mountain [...] Read more.

In this study, we investigate the existence and multiplicity of solutions for a fractional discrete p−Laplacian equation on

Z

. Under suitable hypotheses on the potential function V and the nonlinearity f, with the aid of Ekeland’s variational principle, via mountain pass lemma, we obtain that this equation exists at least two nonnegative and nontrivial homoclinic solutions when the real parameter

λ > 0

is large enough. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

15 pages, 326 KiB

Open AccessArticle

Gradient and Parameter Dependent Dirichlet (p(x),q(x))-Laplace Type Problem

by Kholoud Saad Albalawi, Nadiyah Hussain Alharthi and Francesca Vetro

Mathematics 2022, 10(8), 1336; https://doi.org/10.3390/math10081336 - 18 Apr 2022

Cited by 10 | Viewed by 1280

Abstract

We analyze a Dirichlet

(p (x), μ q (x))

-Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter

μ

varies on [...] Read more.

We analyze a Dirichlet

(p (x), μ q (x))

-Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter

μ

varies on the non-negative real axis. The results are obtained by applying the properties of pseudomonotone operators, jointly with certain a priori estimates. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

19 pages, 310 KiB

Open AccessArticle

A Krasnoselskii–Ishikawa Iterative Algorithm for Monotone Reich Contractions in Partially Ordered Banach Spaces with an Application

by Nawab Hussain, Saud M. Alsulami and Hind Alamri

Mathematics 2022, 10(1), 76; https://doi.org/10.3390/math10010076 - 27 Dec 2021

Cited by 2 | Viewed by 1824

Abstract

Iterative algorithms have been utilized for the computation of approximate solutions of stationary and evolutionary problems associated with differential equations. The aim of this article is to introduce concepts of monotone Reich and Chatterjea nonexpansive mappings on partially ordered Banach spaces. We describe sufficient conditions for the existence of an approximate fixed-point sequence (AFPS) and prove certain fixed-point results using the Krasnoselskii–Ishikawa iterative algorithm. Moreover, we present some interesting examples to highlight the superiority of our results. Lastly, we provide both weak and strong convergence results for such mappings and consider an application of our results to prove the existence of a solution to an initial value problem. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

10 pages, 267 KiB

Open AccessArticle

On the Oscillation of Solutions of Differential Equations with Neutral Term

by Fatemah Mofarreh, Alanoud Almutairi, Omar Bazighifan, Mohammed A. Aiyashi and Alina-Daniela Vîlcu

Mathematics 2021, 9(21), 2709; https://doi.org/10.3390/math9212709 - 25 Oct 2021

Cited by 4 | Viewed by 1242

Abstract

In this work, new criteria for the oscillatory behavior of even-order delay differential equations with neutral term are established by comparison technique, Riccati transformation and integral averaging method. The presented results essentially extend and simplify known conditions in the literature. To prove the [...] Read more.

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

17 pages, 310 KiB

Open AccessArticle

On Some New Weighted Steffensen-Type Inequalities on Time Scales

by Ahmed A. El-Deeb, Omar Bazighifan and Jan Awrejcewicz

Mathematics 2021, 9(21), 2670; https://doi.org/10.3390/math9212670 - 21 Oct 2021

Cited by 8 | Viewed by 927

Abstract

The motivation of this paper is to explore some new inequalities of Steffensen-type which were demonstrated by Pečarić and Kalamir in 2014. The main idea is to investigate a class of certain inequalities by employing diamond-

α

dynamic integral on time scales. In [...] Read more.

α

dynamic integral on time scales. In addition, to obtain some new inequalities as special cases, we also extend our results to continuous and discrete calculations. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

14 pages, 1061 KiB

Open AccessArticle

Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations

by Mohamed M. Mousa and Fahad Alsharari

Mathematics 2021, 9(18), 2244; https://doi.org/10.3390/math9182244 - 12 Sep 2021

Cited by 3 | Viewed by 1520

Abstract

In this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

► Show Figures

Journal Menu

Journal Browser

Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (16 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI