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Symmetry
Special Issues
Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems
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Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1770

Special Issue Editors

Prof. Dr. Xiaoling Han

E-Mail Website
Guest Editor
College of Mathematics and Statistics, Northwest Normal University China, Lanzhou 730070, China
Interests: nonlinear ordinary differential equations; fractional equations; discrete dynamical system
Prof. Dr. Chenghua Gao

E-Mail Website
Guest Editor
Department of Mathematics, Northwest Normal University China, Lanzhou 730070, China
Interests: spectra of linear differential/difference operators; bifurcation phenomena of solutions to nonlinear problems

Special Issue Information

Dear Colleagues,

The study of fractional differential equations and their applications has had a long history with achievements and challenges, and continues to stand among the mainstays of contemporary mathematics. We know that symmetry is a fundamental phenomenon in nature and all sciences. There are many symmetry problems in ordinary differential equations, such as Lie symmetry and radial symmetry. The aim of this Special Issue in Symmetry is to study all kinds of symmetry problems in fractional differential equations, for example, radial symmetry of solutions for fractional parabolic equations. It will be devoted to topics in fractional differential equations, fractional order systems, and their advanced applications.

Prof. Dr. Xiaoling Han
Prof. Dr. Chenghua Gao
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

  • fractional differential equations
  • delay differential equations
  • functional equations
  • partial differential equations
  • stochastic differential equations
  • integral equations
  • dynamical systems
  • applications of fixed-point theorems to nonlinear equations

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

Published Papers (3 papers)

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Research

27 pages, 665 KiB  
Article
Study of Stability and Simulation for Nonlinear (k, ψ)-Fractional Differential Coupled Laplacian Equations with Multi-Point Mixed (k, ψ)-Derivative and Symmetric Integral Boundary Conditions
by Xiaojun Lv and Kaihong Zhao
Symmetry 2025, 17(3), 472; https://doi.org/10.3390/sym17030472 - 20 Mar 2025
Viewed by 159
Abstract
The (k,ψ)-fractional derivative based on the k-gamma function is a more general version of the Hilfer fractional derivative. It is widely used in differential equations to describe physical phenomena, population dynamics, and biological genetic memory problems. In [...] Read more.
The (k,ψ)-fractional derivative based on the k-gamma function is a more general version of the Hilfer fractional derivative. It is widely used in differential equations to describe physical phenomena, population dynamics, and biological genetic memory problems. In this article, we mainly study the 4m+2-point symmetric integral boundary value problem of nonlinear (k,ψ)-fractional differential coupled Laplacian equations. The existence and uniqueness of solutions are obtained by the Krasnosel’skii fixed-point theorem and Banach’s contraction mapping principle. Furthermore, we also apply the calculus inequality techniques to discuss the stability of this system. Finally, three interesting examples and numerical simulations are given to further verify the correctness and effectiveness of the conclusions. Full article
(This article belongs to the Special Issue Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems)
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20 pages, 309 KiB  
Article
Fractional Optimal Control Problem for Symmetric System Involving Distributed-Order Atangana–Baleanu Derivatives with Non-Singular Kernel
by Bahaa Gaber Mohamed and Ahlam Hasan Qamlo
Symmetry 2025, 17(3), 417; https://doi.org/10.3390/sym17030417 - 10 Mar 2025
Viewed by 397
Abstract
The objective of this work is to discuss and thoroughly analyze the fractional variational principles of symmetric systems involving distributed-order Atangana–Baleanu derivatives. A component of distributed order, the fractional Euler–Lagrange equations of fractional Lagrangians for constrained systems are studied concerning Atangana–Baleanu derivatives. We [...] Read more.
The objective of this work is to discuss and thoroughly analyze the fractional variational principles of symmetric systems involving distributed-order Atangana–Baleanu derivatives. A component of distributed order, the fractional Euler–Lagrange equations of fractional Lagrangians for constrained systems are studied concerning Atangana–Baleanu derivatives. We give a general formulation and a solution technique for a class of fractional optimal control problems (FOCPs) for such systems. The dynamic constraints are defined by a collection of FDEs, and the performance index of an FOCP is considered a function of the control variables and the state. The formula for fractional integration by parts, the Lagrange multiplier, and the calculus of variations are used to obtain the Euler–Lagrange equations for the FOCPs. Full article
(This article belongs to the Special Issue Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems)
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13 pages, 270 KiB  
Article
Existence of Positive Solutions for Singular Difference Equations with Nonlinear Boundary Conditions
by Hua Luo and Alhussein Mohamed
Symmetry 2024, 16(10), 1313; https://doi.org/10.3390/sym16101313 - 5 Oct 2024
Viewed by 704
Abstract
In this paper, we delve into a discrete nonlinear singular semipositone problem, characterized by a nonlinear boundary condition. The nonlinearity, given by f(u)−auα with α>0, exhibits a singularity at u=0 and [...] Read more.
In this paper, we delve into a discrete nonlinear singular semipositone problem, characterized by a nonlinear boundary condition. The nonlinearity, given by f(u)−auα with α>0, exhibits a singularity at u=0 and tends towards −∞ as u approaches 0+. By constructing some suitable auxiliary problems, the difficulty that arises from the singularity and semipositone of nonlinearity and the lack of a maximum principle is overcome. Subsequently, employing the Krasnosel’skii fixed-point theorem, we determine the parameter range that ensures the existence of at least one positive solution and the emergence of at least two positive solutions. Furthermore, based on our existence results, one can obtain the symmetry of the solutions after adding some symmetric conditions on the given functions by using a standard argument. Full article
(This article belongs to the Special Issue Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems)
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