Application of Symmetry/Asymmetry in Fractional Differential Equations

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

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 4943

Special Issue Editors


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Guest Editor
Department of Solar Materials, Renewable Energy Institute, National Autonomous University of Mexico, Priv. Xochicalco s/n. Col. Centro, Temixco Morelos, Mexico
Interests: applied mathematics; nonlinear dynamics; complex systems; fractional differential equations; fractional order system; signal processing; discrete fractional order systems; process control; bioelectromagnetism

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Co-Guest Editor
Department of Mathematics, Balikesir University, Balikesir, Turkey
Interests: fractional calculus; optimal control theory; fractional thermoelasticity; numerical analysis

Special Issue Information

Dear Colleagues,

Due to its applicability in many domains of applied sciences such as mathematics, engineering, chemistry, physics, finance, and social sciences, researchers are interested in the exploration of symmetry and asymmetry fractional calculus in recent decades. These examples demonstrate the value of fractional calculus. As a result, various fractional derivative definitions have arisen in the literature. Used to provide more realistic representations of real-world events, a few well-known examples of fractional derivatives include Riemann–Liouville, modified Riemann–Liouville, Riesz, Grunwald–Letnikov, Caputo, ErdélyiKober, and Hadmard and Marchaud.

Fractional calculus was proposed very recently. Although it has always played an important role in mathematics, it has recently grown in significance in several branches, including but not limited to topological indices, polynomials in graphs,  molecular descriptors, differential of graphs, alliances in graphs, domination theory, complex systems, symmetry, asymmetry,  geometry, fractional differential equations,  fractional integral inequalities, and more. Symmetry and asymmetry fractional differential equations are well known as effective tools for modellng and solving issues involving nonlinear events. Physical processes are specifically mentioned as issues in elasticity theory, when we are dealing with composites consisting of two distinct materials with differing hardening exponents.

The goal of this Special Issue is to attract prominent scholars in these fields so that fresh high-quality research studies on these problems, including their dynamical features can be included, both theoretically and numerically.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Application of Symmetry/ Asymmetry in Fractional Differential Equations” via: MDPI submission system. Please contact the collection editor or the journal editor ([email protected]) for any queries. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Gómez Aguilar José Francisco
Dr. Derya Avcı
Guest Editors

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Keywords

  • new theories and application for symmetry and asymmetry fractional calculus
  • fractional-order biological models
  • fractional-order physical models
  • fractional-order systems
  • application of symmetry fractional-order systems
  • new iterative technique for symmetry and asymmetry fractional order systems
  • applications of fractional calculus in medical and engineering
  • fractional-order wireless sensor network models
  • numerical methods for delta and nabla discrete fractional operators

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Published Papers (3 papers)

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Research

12 pages, 258 KiB  
Article
A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind
by Waseem Ahmad Khan and Maryam Salem Alatawi
Symmetry 2023, 15(1), 136; https://doi.org/10.3390/sym15010136 - 3 Jan 2023
Cited by 5 | Viewed by 1167
Abstract
In this study, we introduce modified degenerate Changhee–Genocchi polynomials of the second kind, and analyze some properties by providing several relations and applications. We first attain diverse relations and formulas covering addition formulas, recurrence rules, implicit summation formulas, and relations with the earlier [...] Read more.
In this study, we introduce modified degenerate Changhee–Genocchi polynomials of the second kind, and analyze some properties by providing several relations and applications. We first attain diverse relations and formulas covering addition formulas, recurrence rules, implicit summation formulas, and relations with the earlier polynomials in the literature. By using their generating function, we derive some new relations, including the Stirling numbers of the first and second kinds. Moreover, we introduce modified higher-order degenerate Changhee–Genocchi polynomials of the second kind. We also derive some new identities and properties of this type of polynomials. Full article
11 pages, 336 KiB  
Article
On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions
by Ramasamy Arul, Panjayan Karthikeyan, Kulandhaivel Karthikeyan, Palanisamy Geetha, Ymnah Alruwaily, Lamya Almaghamsi and El-sayed El-hady
Symmetry 2023, 15(1), 5; https://doi.org/10.3390/sym15010005 - 20 Dec 2022
Cited by 5 | Viewed by 1297
Abstract
We propose a solution to the symmetric nonlinear Ψ-Caputo fractional integro differential equations involving non-instantaneous impulsive boundary conditions. We investigate the existence and uniqueness of the solution for the proposed problem. Banach contraction theorem is employed to prove the uniqueness results, while [...] Read more.
We propose a solution to the symmetric nonlinear Ψ-Caputo fractional integro differential equations involving non-instantaneous impulsive boundary conditions. We investigate the existence and uniqueness of the solution for the proposed problem. Banach contraction theorem is employed to prove the uniqueness results, while Krasnoselkii’s fixed point technique is used to prove the existence results. Additionally, an example is used to explain the results. In this manner, our results represent generalized versions of some recent interesting contributions. Full article
11 pages, 364 KiB  
Article
Double Controlled Quasi Metric Like Spaces
by Salma Haque, Asma Karoui Souayah, Nabil Mlaiki and Doaa Rizk
Symmetry 2022, 14(3), 618; https://doi.org/10.3390/sym14030618 - 19 Mar 2022
Cited by 3 | Viewed by 1835
Abstract
In this article, we present a generalization of the double controlled metric like spaces, called quasi double controlled metric like spaces, by assuming that the symmetric condition is not necessary satisfied. Moreover, the self distance is not necessary zero. Full article
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