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Symmetry
Special Issues
Differential/Difference Equations and Its Application: Volume II
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Differential/Difference Equations and Its Application: Volume II

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

Deadline for manuscript submissions: closed (31 October 2024) | Viewed by 3089

Special Issue Editor

Prof. Dr. Youssef N. Raffoul

E-Mail Website
Guest Editor
Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469-2316, USA
Interests: mathematics; differential/difference equations; integral equations and dynamical systems on time scales
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the great success of our Special Issue "Differential/Difference Equations and Its Application" we decided to set up a second volume. 

There is no doubt that differential equations play important roles in modeling real world problems owing to their extensive use in several fields, such as physics, statistics, control theory, electrical circuit theory, dynamical systems, economics, and biology.

The main objective of this Special Issue is to foster links between basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences. This should provide a channel of communication between scientists and practitioners working in the field of complex systems analysis and will stimulate the development and use of a continuous and discrete dynamical approach.

This Special Issue complements the aim of the journal since symmetry plays an important role in the study of both ordinary differential equations and partial differential equations.

The major aim of this Special Issue is for authors from scientific disciplines to publish high-quality research on recent developments in the field of differential and difference systems and related applications. Topics for this Special Issue may include but are not limited to the following:

  • Symmetry method in differential equations;
  • Symmetry method in partial differential equations;
  • Boundary value problems;
  • Boundary value problems at resonance;
  • Upper and lower solutions;
  • Inequalities;
  • Transformations;
  • Qualitative analysis of functional dynamical systems with finite and infinite delays. Such analyses may include stability, boundedness, existence, and uniqueness of solutions and the existence of periodic solutions;
  • Integrodynamical system on time scales;
  • Numerical solutions of dynamical systems;
  • The topics on the application of differential and difference systems may include economics models utilizing optimal control theory and the development of new population models.

Welcome to read the publications in "Differential/Difference Equations and Its Application" at https://www.mdpi.com/journal/symmetry/special_issues/Differential_Difference_Equations_Its_Application.

Prof. Dr. Youssef N. Raffoul
Guest Editor

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

  • symmetry
  • ordinary
  • partial
  • transformations
  • time scales
  • Lyapunov functions/functionals
  • dynamical systems

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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Research

12 pages, 298 KiB  
Article
Enhanced Oscillation Criteria for Non-Canonical Second-Order Advanced Dynamic Equations on Time Scales
by Ahmed M. Hassan, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani and Samy E. Affan
Symmetry 2024, 16(11), 1457; https://doi.org/10.3390/sym16111457 - 2 Nov 2024
Viewed by 459
Abstract
This study aims to establish novel iterative oscillation criteria for second-order half-linear advanced dynamic equations in non-canonical form. The results extend and enhance recently established criteria for this type of equation by various authors and also encompass the classical criteria for related ordinary [...] Read more.
This study aims to establish novel iterative oscillation criteria for second-order half-linear advanced dynamic equations in non-canonical form. The results extend and enhance recently established criteria for this type of equation by various authors and also encompass the classical criteria for related ordinary differential equations. Our methodology involves transforming the non-canonical equation into its corresponding canonical form. The inherent symmetry of these canonical forms plays a pivotal role in deriving our new criteria. By employing techniques from the theory of symmetric differential equations and utilizing symmetric functions, we establish precise conditions for oscillation. Several illustrative examples highlight the accuracy, applicability, and versatility of our results. Full article
(This article belongs to the Special Issue Differential/Difference Equations and Its Application: Volume II)
17 pages, 423 KiB  
Article
Numerical Solution of the Linear Fractional Delay Differential Equation Using Gauss–Hermite Quadrature
by Salma Aljawi, Sarah Aljohani, Kamran, Asma Ahmed and Nabil Mlaiki
Symmetry 2024, 16(6), 721; https://doi.org/10.3390/sym16060721 - 10 Jun 2024
Viewed by 687
Abstract
Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the [...] Read more.
Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation. Full article
(This article belongs to the Special Issue Differential/Difference Equations and Its Application: Volume II)
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23 pages, 761 KiB  
Article
Improving Performance of Differential Evolution Using Multi-Population Ensemble Concept
by Aadil Bashir, Qamar Abbas, Khalid Mahmood, Sultan Alfarhood, Mejdl Safran and Imran Ashraf
Symmetry 2023, 15(10), 1818; https://doi.org/10.3390/sym15101818 - 25 Sep 2023
Cited by 1 | Viewed by 1330
Abstract
Differential evolution (DE) stands out as a straightforward yet remarkably powerful evolutionary algorithm employed for real-world problem-solving purposes. In the DE algorithm, few parameters are used, and the population is evolved by applying various operations. It is difficult in evolutionary computation algorithms to [...] Read more.
Differential evolution (DE) stands out as a straightforward yet remarkably powerful evolutionary algorithm employed for real-world problem-solving purposes. In the DE algorithm, few parameters are used, and the population is evolved by applying various operations. It is difficult in evolutionary computation algorithms to maintain population diversity. The main issue is the sub-population of the DE algorithm that helps improve convergence speed and escape from the local optimum. Evolving sub-populations by maintaining diversity is an important issue in the literature that is considered in this research. A solution is proposed that uses sub-populations to promote greater diversity within the population and improve the algorithm performance. DE, heterogeneous distributed differential evolution (HDDE), multi-population ensemble differential evolution (MPEDE), and the proposed improved multi-population ensemble differential evolution (IMPEDE) are implemented using parameter settings; population sizes of 100 NP, 150 NP, and 200 NP; and dimensions of 10D, 30D, and 50D for performance comparison. Different combinations of mutations are used to generate the simulated results. The simulation results are generated using 1000, 3000, and 5000 iterations. Experimental outcomes show the superior results of the proposed IMPEDE over existing algorithms. The non-parametric significance Friedman test confirms that there is a significant difference in the performance of the proposed algorithm and other algorithms used in this study by considering a 0.05 level of significance using six benchmark functions. Full article
(This article belongs to the Special Issue Differential/Difference Equations and Its Application: Volume II)
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