Fractional Differential Equations and Dynamical Systems

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 April 2025) | Viewed by 970

Special Issue Editors


E-Mail Website
Guest Editor
Department of Mathematics, University of South Australia, Adelaide, SA 5000, Australia
Interests: dynamical systems; fractional differential equations

E-Mail Website
Guest Editor
Istituto per le Applicazioni del Calcolo “M. Picone” Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Rome, Italy
Interests: differential models; numerical methods and computer simulation for dynamical complex systems with applications in biomedicine; conservation of cultural heritage and fluid dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will explore new research and trends in dynamical systems focused on problems involving fractional differential equations. The motivation of fractional order equations and the theory are able to describe complex processors and systems, including the effect of “memory” on describing a system by considering fractional derivatives and differences instead of integer jumps in the growth of physical processors. They appear in a wide range of scientific applications in the fields of engineering, physics, chemistry, and biology, as well as in financial mathematics and health informatics. There is a strong demand to develop both functional analysis theory and approximation schemes to find both analytical solutions and their approximations. There has been rapid growth and interest in both of these areas in the last twenty years, and as society continually tangibly progresses to the computing age, understanding and predicting real-world phenomena are crucial, and fractional calculus is providing an avenue at the forefront of this. This Special Issue will focus on manuscripts that enrich and complement the area of fractional calculus and dynamical systems. The following areas are of significance and interest to this Special Issue, but it is not limited to this list: 

  • New numerical approximation schemes for time fractional differential equations;
  • Theory of stochastic fractional differential equations and schemes;
  • New qualitative fractional order theory in dynamical systems;
  • Improvements to discrete fractional calculus and applications to dynamical systems;
  • Theory of fractional integrals, operators, and derivatives to describe problems;
  • Asymptotic theory and numerical methods for fractional differential equations;
  • Higher-order fractional differential equations and applications to boundary value problems;
  • Fractional calculus and its application to differential geometry and mathematical physics.

Dr. Nicholas Fewster-Young
Dr. Gabriella Bretti
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 differential equations
  • dynamical systems
  • fractional calculus
  • fractional integrals

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

19 pages, 3943 KiB  
Article
Dynamics of Abundant Wave Solutions to the Fractional Chiral Nonlinear Schrodinger’s Equation: Phase Portraits, Variational Principle and Hamiltonian, Chaotic Behavior, Bifurcation and Sensitivity Analysis
by Yu Tian, Kang-Hua Yan, Shao-Hui Wang, Kang-Jia Wang and Chang Liu
Axioms 2025, 14(6), 438; https://doi.org/10.3390/axioms14060438 - 3 Jun 2025
Viewed by 331
Abstract
The central objective of this study is to develop some different wave solutions and perform a qualitative analysis on the nonlinear dynamics of the time-fractional chiral nonlinear Schrodinger’s equation (NLSE) in the conformable sense. Combined with the semi-inverse method (SIM) and traveling wave [...] Read more.
The central objective of this study is to develop some different wave solutions and perform a qualitative analysis on the nonlinear dynamics of the time-fractional chiral nonlinear Schrodinger’s equation (NLSE) in the conformable sense. Combined with the semi-inverse method (SIM) and traveling wave transformation, we establish the variational principle (VP). Based on this, the corresponding Hamiltonian is constructed. Adopting the Galilean transformation, the planar dynamical system is derived. Then, the phase portraits are plotted and the bifurcation analysis is presented to expound the existence conditions of the various wave solutions with the different shapes. Furthermore, the chaotic phenomenon is probed and sensitivity analysis is given in detail. Finally, two powerful tools, namely the variational method (VM) which stems from the VP and Ritz method, as well as the Hamiltonian-based method (HBM) that is based on the energy conservation theory, are adopted to find the abundant wave solutions, which are the bell-shape soliton (bright soliton), W-shape soliton (double-bright solitons or double bell-shaped soliton) and periodic wave solutions. The shapes of the attained new diverse wave solutions are simulated graphically, and the impact of the fractional order δ on the behaviors of the extracted wave solutions are also elaborated. To the authors’ knowledge, the findings of this research have not been reported elsewhere and can enable us to gain a profound understanding of the dynamics characteristics of the investigative equation. Full article
(This article belongs to the Special Issue Fractional Differential Equations and Dynamical Systems)
Show Figures

Figure 1

Back to TopTop