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Axioms
Special Issues
Nonlinear Fractional Differential Equations: Theory and Applications
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Nonlinear Fractional Differential Equations: Theory and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 809

Special Issue Editors

Dr. Jiawei He

E-Mail Website
Guest Editor
School of Mathematics and Information Science, Guangxi University, Nanning 530004, China
Interests: fractional evolution equations; partial differential equations; differential equations; dynamical systems
Dr. Junfang Zhao

E-Mail Website
Guest Editor
School of Science, China University of Geosciences, Beijing 100083, China
Interests: boundary value problem; partial differential equations; critical points theory; physical information neural network; machine learning

Special Issue Information

Dear Colleagues,

Fractional calculus is a sub-branch of mathematics and applied mathematics, and the fractional problem has become an absorbing field for scientists and mathematicians due to its widespread applications in modeling, engineering, mathematical biology, financial modeling, fluid flows, and so on.

The Special Issue aims to bring together the latest research and developments in the field of nonlinear fractional calculus and nonlinear partial differential equations. This area of study has become increasingly important due to its ability to model complex systems that exhibit memory and hereditary properties, which are often encountered in real-world applications. The issue will feature articles that cover a wide range of topics, including the theoretical foundations of nonlinear fractional differential equations, and their applications in various fields such as physics, engineering, biology, and finance. The goal is to provide an overview of the current state of research in this area and to highlight the potential for future developments and applications. This Special Issue will be of interest to researchers, academics, and practitioners who are involved in the study of nonlinear dynamics, fractional calculus, partial differential equations, and their applications in various scientific and engineering disciplines.

Dr. Jiawei He
Dr. Junfang Zhao
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. Axioms 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 calculus and applications
  • fractional order nonlinear systems
  • partial differential equations
  • integrodifferential equations
  • critical point theory
  • control theory
  • continuous and discrete dynamical systems
  • initial and boundary value problems
  • stability theory

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

Published Papers (2 papers)

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Research

18 pages, 293 KiB  
Article
Existence and Controls for Fractional Evolution Equations
by Ying Chen and Yong Zhou
Axioms 2025, 14(5), 329; https://doi.org/10.3390/axioms14050329 - 24 Apr 2025
Viewed by 130
Abstract
In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals [...] Read more.
In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals is studied, and the existence of optimal control pairs is proven. Finally, by constructing a corresponding Gramian controllability operator using the solution operator, a sufficient condition is provided for the existence of approximate controllability of the corresponding problem. Full article
(This article belongs to the Special Issue Nonlinear Fractional Differential Equations: Theory and Applications)
13 pages, 272 KiB  
Article
Existence and Attractivity of Mild Solutions for Fractional Diffusion Equations Involving the Regularized ψ-Hilfer Fractional Derivatives
by Luyao Wang, Yuhang Jin, Wenchang He and Jia Mu
Axioms 2025, 14(2), 79; https://doi.org/10.3390/axioms14020079 - 22 Jan 2025
Viewed by 519
Abstract
The regularized ψ-Hilfer derivative within the sense of Caputo is an improved version of the ψ-Hilfer fractional derivative, primarily because it addresses the issue where the initial conditions of problems involving the ψ-Hilfer fractional derivative lack clear physical significance unless [...] Read more.
The regularized ψ-Hilfer derivative within the sense of Caputo is an improved version of the ψ-Hilfer fractional derivative, primarily because it addresses the issue where the initial conditions of problems involving the ψ-Hilfer fractional derivative lack clear physical significance unless p=1. This article’s main contribution is the use of the ψ-Laplace transform, which is the first to provide an explicit expression for mild solutions to the fractional diffusion equations with the regularized ψ-Hilfer derivative. Additionally, we investigate the existence and attractivity of mild solutions for fractional diffusion equations involving the regularized ψ-Hilfer fractional derivatives. Finally, we provide two examples to illustrate our main results. Full article
(This article belongs to the Special Issue Nonlinear Fractional Differential Equations: Theory and Applications)
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