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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: 28 February 2025 | Viewed by 446

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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Published Papers (1 paper)

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Research

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 349
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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