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Symmetry
Special Issues
The Qualitative Theory of Functional Differential Equations and their Applications
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The Qualitative Theory of Functional Differential Equations and their Applications

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

Deadline for manuscript submissions: 15 May 2024 | Viewed by 9328

Special Issue Editors

Dr. Osama Moaaz

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Interests: differental equations; numerical analysis; analysis; applied mathematics; nonlinear dynamics; mathematical modelling; mathematical analysis; stability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Higinio Ramos

E-Mail Website
Guest Editor
1. Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
2. Escuela Politécnica Superior de Zamora, Universidad de Salamanca, Campus Viriato, 49029 Zamora, Spain
Interests: numerical solution of differential equations; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Functional differential equations arise in many applied sciences fields. Very recently, there was an active research movement that mainly and significantly developed methods and techniques for studying the qualitative theory differential equations.

Delay differential equations (DDE) as a subclass of functional differential equations take into account the dependence on the history of the system, which results in predicting the future in a more reliable and efficient way. Neutral delay differential equations arise in various phenomena, including problems concerning electric networks containing lossless transmission lines (as in high-speed computers where such lines are used to interconnect switching circuits), in the study of vibrating masses attached to an elastic bar or in the solution of variational problems with time delays, or in the theory of automatic control and in neuromechanical systems in which inertia plays a major role.

In recent decades, various models of difference and differential equations have been proposed in different sciences, strongly motivating research in the qualitative theory of difference and differential equations. Symmetry ideas are often missing in these studies, but they help us find the most suitable approach to studying difference and differential equations and suggest the correct directions for future developments.

This issue will select and publish works that contribute to the development of the study of the qualitative behavior of functional differential equations. This Special Issue will bring together state-of-the-art theoretical research and its applications in mathematical models. Please note that all submitted papers must be within the general scope of the Symmetry journal.

Dr. Osama Moaaz
Prof. Dr. Higinio Ramos
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

  • Functional differential equations 
  • Delay/neutral/advanced differential equations 
  • Ordinary differential equation 
  • Difference equation
  • Partial differential equation 
  • Symmetry in differential equations 
  • Numerical analysis, numerical modeling 
  • Approximation, stability, oscillation, boundedness, periodicity, and asymptotic properties

Published Papers (7 papers)

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Research

11 pages, 282 KiB  
Article
Higher-Order Delay Differential Equation with Distributed Deviating Arguments: Improving Monotonic Properties of Kneser Solutions
by Shaimaa Elsaeed, Osama Moaaz, Ghada AlNemer and Elmetwally M. Elabbasy
Symmetry 2023, 15(2), 502; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15020502 - 14 Feb 2023
Viewed by 780
Abstract
This study aims to investigate the oscillatory behavior of the solutions of an even-order delay differential equation with distributed deviating arguments. We first study the monotonic properties of positive decreasing solutions or the so-called Kneser solutions. Then, by iterative deduction, we improve these [...] Read more.
This study aims to investigate the oscillatory behavior of the solutions of an even-order delay differential equation with distributed deviating arguments. We first study the monotonic properties of positive decreasing solutions or the so-called Kneser solutions. Then, by iterative deduction, we improve these properties, which enables us to apply them more than once. Finally, depending on the symmetry between the positive and negative solutions of the studied equation and by combining the new condition for the exclusion of Kneser solutions with some well-known results in the literature, we establish a new standard for the oscillation of the investigated equation. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
28 pages, 360 KiB  
Article
Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces
by Agilan Pasupathi, Julietraja Konsalraj, Nahid Fatima, Vallinayagam Velusamy, Nabil Mlaiki and Nizar Souayah
Symmetry 2022, 14(8), 1700; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081700 - 16 Aug 2022
Cited by 6 | Viewed by 987
Abstract
Over the last few decades, a certain interesting class of functional equations were developed while obtaining the generating functions of many system distributions. This class of equations has numerous applications in many modern disciplines such as wireless networks and communications. The Ulam stability [...] Read more.
Over the last few decades, a certain interesting class of functional equations were developed while obtaining the generating functions of many system distributions. This class of equations has numerous applications in many modern disciplines such as wireless networks and communications. The Ulam stability theorem can be applied to numerous functional equations in investigating the stability when approximated in Banach spaces, Banach algebra, and so on. The main focus of this study is to analyse the relationship between functional equations, Hyers–Ulam–Rassias stability, Banach space, quasi-beta normed spaces, and fixed-point theory in depth. The significance of this work is the incorporation of the stability of the generalised additive functional equation in Banach space and quasi-beta normed spaces by employing concrete techniques like direct and fixed-point theory methods. They are powerful tools for narrowing down the mathematical models that describe a wide range of events. Some classes of functional equations, in particular, have lately emerged from a variety of applications, such as Fourier transforms and the Laplace transforms. This study uses linear transformation to explain our functional equations while providing suitable examples. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
15 pages, 316 KiB  
Article
On Unique Solvability of a Multipoint Boundary Value Problem for Systems of Integro-Differential Equations with Involution
by Kairat I. Usmanov, Batirkhan Kh. Turmetov and Kulzina Zh. Nazarova
Symmetry 2022, 14(8), 1626; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081626 - 07 Aug 2022
Cited by 2 | Viewed by 767
Abstract
In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, the parameterization method is used. Based on the parametrization method, the studied problem is decomposed into two parts, i.e., into [...] Read more.
In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, the parameterization method is used. Based on the parametrization method, the studied problem is decomposed into two parts, i.e., into the Cauchy problem and a system of linear equations. Necessary and sufficient conditions for the unique solvability of the studied problem are determined. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
14 pages, 303 KiB  
Article
On Some Important Class of Dynamic Hilbert’s-Type Inequalities on Time Scales
by Hassan M. El-Owaidy, Ahmed A. El-Deeb, Samer D. Makharesh, Dumitru Baleanu and Clemente Cesarano
Symmetry 2022, 14(7), 1395; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14071395 - 07 Jul 2022
Cited by 1 | Viewed by 1012
Abstract
In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved [...] Read more.
In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, Hölder inequality, and Jensen’s inequality on time scales. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
9 pages, 281 KiB  
Article
On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution
by Abdissalam Sarsenbi and Abdizhahan Sarsenbi
Symmetry 2021, 13(10), 1972; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13101972 - 19 Oct 2021
Cited by 8 | Viewed by 1500
Abstract
We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in the terms of the boundary conditions. Uniform equiconvergence [...] Read more.
We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in the terms of the boundary conditions. Uniform equiconvergence of spectral expansions related to the second-order differential equations with involution:−y″(x)+αy″(−x)+qxyx=λyx,−1<x<1, with the boundary conditions y′−1+b1y−1=0,y′1+b2y1=0, is obtained. As a corollary, it is proved that the eigenfunctions of the perturbed boundary value problems form the basis in L2(−1,1) for any complex-valued coefficient q(x)∈L1(−1,1). Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
20 pages, 349 KiB  
Article
On Eigenfunctions and Eigenvalues of a Nonlocal Laplace Operator with Multiple Involution
by Batirkhan Turmetov and Valery Karachik
Symmetry 2021, 13(10), 1781; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13101781 - 25 Sep 2021
Cited by 9 | Viewed by 1235
Abstract
We study the eigenfunctions and eigenvalues of the boundary value problem for the nonlocal Laplace equation with multiple involution. An explicit form of the eigenfunctions and eigenvalues for the unit ball are obtained. A theorem on the completeness of the eigenfunctions of the [...] Read more.
We study the eigenfunctions and eigenvalues of the boundary value problem for the nonlocal Laplace equation with multiple involution. An explicit form of the eigenfunctions and eigenvalues for the unit ball are obtained. A theorem on the completeness of the eigenfunctions of the problem under consideration is proved. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
13 pages, 262 KiB  
Article
New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions
by Shyam Sundar Santra, Khaled Mohamed Khedher, Kamsing Nonlaopon and Hijaz Ahmad
Symmetry 2021, 13(6), 934; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13060934 - 25 May 2021
Cited by 9 | Viewed by 1345
Abstract
The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are [...] Read more.
The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
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