Fractional Nonlinear Dynamics in Science and Engineering

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 620

Special Issue Editors


E-Mail Website
Guest Editor
1. Department of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia
2. Department of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes 20131, Mexico
Interests: fractional calculus; fractional analysis; numerical methods for fractional differential equations; nonlinear fractional analysis; simulation of fractional systems; nonlinear systems
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics, University of Patras, 26500 Patras, Greece
Interests: nonlinear dynamical systems; nonlinear fractional models; nonlinear systems and complex systems; ordinary differential equations and integrability; Hamiltonian lattices; chaos; fractals and complexity; theory and applications

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to provide an opportunity for researchers to report on recent progress in the dynamics of nonlinear fractional systems arising in natural, engineering, and social sciences. Both the qualitative features of solutions of fractional nonlinear dynamical models and the analysis of simulation techniques used to approximate these solutions are of special interest. Papers that study the existence and uniqueness of solutions of nonlinear fractional systems as well as relevant features of solution spaces are especially welcome. Works that emphasize the usefulness of fractional models in accurately simulating the dynamics of complex systems in physics, engineering, and the social sciences are solicited for this Special Issue.

This issue will not place emphasis on the mathematical modeling of particular applications of nonlinear systems, but rather on the investigation of analytical features of the solutions of dynamical systems and the advancement of mathematical techniques used to simulate them. Both deterministic and stochastic models arising in natural and social sciences will be considered, and pertinent applications to the resolution of practical problems will be encouraged. The topics of this Special Issue include, but are not limited to, the following:

  • Deterministic and stochastic nonlinear fractional models;
  • Fractional nonlinear systems and simulation techniques;
  • The existence and uniqueness of relevant solutions;
  • Approximation theory;
  • Discrete methods for the simulation of nonlinear models (finite differences, finite elements, finite volumes, quadrature methods, etc.);
  • Structure-preserving models;
  • The efficiency, accuracy, stability, and convergence of solutions;
  • Positivity, boundedness, convexity, and monotonicity properties of solutions;
  • Mathematical applications across scientific boundaries.

Prof. Dr. Jorge E. Macías Díaz
Prof. Dr. Tassos Bountis
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. Fractal and Fractional 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 2700 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

  • nonlinear fractional models
  • deterministic and stochastic models
  • fractional nonlinear systems
  • dynamics of fractional nonlinear systems
  • complex systems

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

29 pages, 2344 KiB  
Article
A Discrete Model to Solve a Bifractional Dissipative Sine-Gordon Equation: Theoretical Analysis and Simulations
by Dagoberto Mares-Rincón, Siegfried Macías, Jorge E. Macías-Díaz, José A. Guerrero-Díaz-de-León and Tassos Bountis
Fractal Fract. 2025, 9(8), 498; https://doi.org/10.3390/fractalfract9080498 - 30 Jul 2025
Viewed by 332
Abstract
In this work, we consider a generalized form of the classical (2+1)-dimensional sine-Gordon system. The mathematical model considers a generalized reaction term, and the two-dimensional Laplacian includes the presence of space-fractional derivatives of the Riesz type with two [...] Read more.
In this work, we consider a generalized form of the classical (2+1)-dimensional sine-Gordon system. The mathematical model considers a generalized reaction term, and the two-dimensional Laplacian includes the presence of space-fractional derivatives of the Riesz type with two different differentiation orders in general. The system is equipped with a conserved quantity that resembles the energy functional in the integer-order scenario. We propose a numerical model to approximate the solutions of the fractional sine-Gordon equation. A discretized form of the energy-like quantity is proposed, and we prove that it is conserved throughout the discrete time. Moreover, the analysis of consistency, stability, and convergence is rigorously carried out. The numerical model is implemented computationally, and some computer simulations are presented in this work. As a consequence of our simulations, we show that the discrete energy is approximately conserved throughout time, which coincides with the theoretical results. Full article
(This article belongs to the Special Issue Fractional Nonlinear Dynamics in Science and Engineering)
Show Figures

Figure 1

Back to TopTop