Nonlinear Dynamics, Chaos and Control of Fractional Systems

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

Deadline for manuscript submissions: 31 January 2026 | Viewed by 778

Special Issue Editors


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Guest Editor
Department of Mathematics, Federal Technological University of Parana, Ponta Grossa 84017-220, Brazil
Interests: nonlinear dynamics; chaos control; bifurcation; non-convex optimization; fractal differential equations

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Special Issue Information

Dear Colleagues,

We request submissions to a Special Issue dedicated to the modeling, control and applications of fractional-order nonlinear dynamical systems (FONDS). Fractional-order calculus (FOC), which encompasses systems with non-integer-order dynamics, has its roots in the foundational work of renowned mathematicians such as Euler, Liouville, Riemann, and Letnikov. Fractional derivatives offer a powerful framework for capturing memory effects, providing a more accurate representation of real-world phenomena than traditional integer-order models. As a result, fractional-order systems have been paid increasing attention in various disciplines, including solid mechanics, physics, chemistry, finance, and bioengineering. This Special Issue will highlight recent advances in the theory and application of fractional-order systems, with a particular focus on nonlinear dynamics. We welcome original research articles, review papers, and case studies addressing (but not limited to) the following topics:

  • Nonlinear fractional-order dynamical systems;
  • Control and stability of fractional-order systems;
  • Chaos, bifurcation, and complex behavior in FO systems;
  • Fractals and fractional modeling;
  • Applications to time series and real-world phenomena.

Submissions will undergo rigorous peer review. Authors are encouraged to emphasize both theoretical innovation and practical relevance.

Prof. Dr. Vinícius Piccirillo
Prof. Dr. José Manoel Balthazar
Prof. Dr. Angelo Marcelo Tusset
Prof. Dr. Jeferson José de Lima
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 250 words) can be sent to the Editorial Office for assessment.

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

  • fractional-order systems
  • nonlinear dynamics
  • chaos and bifurcation
  • fractional-order control
  • memory effects
  • time series modeling

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Published Papers (1 paper)

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Research

17 pages, 4947 KB  
Article
On Variable-Order Fractional Discrete Macroeconomic Model: Stability, Chaos, and Complexity
by Ali Aloui, Louiza Diabi, Omar Kahouli, Adel Ouannas, Lilia El Amraoui and Mohamed Ayari
Fractal Fract. 2025, 9(11), 723; https://doi.org/10.3390/fractalfract9110723 - 8 Nov 2025
Viewed by 464
Abstract
Macroeconomic mathematical models are practical instruments structured to carry out theoretical analyses of macroeconomic developments. In this manuscript, the Caputo-like fractional operator of variable order is used to introduce and investigate the mechanism of the discrete macroeconomic model. The nature of the dynamics [...] Read more.
Macroeconomic mathematical models are practical instruments structured to carry out theoretical analyses of macroeconomic developments. In this manuscript, the Caputo-like fractional operator of variable order is used to introduce and investigate the mechanism of the discrete macroeconomic model. The nature of the dynamics was established, and the emergence of chaos using a distinct variable fractional order, especially the stability of the trivial solution, is examined. The findings reveal that the variable-order discrete macroeconomic model displays chaotic dynamics employing bifurcation, the Largest Lyapunov exponent (LEmax), the phase portraits, and the 0–1 test. Furthermore, a complexity analysis is performed to demonstrate the existence of chaos and quantify its complexity using C0 complexity and spectral entropy (SE). These studies show that the suggested variable-order fractional discrete macroeconomic model has more complex features than integer and constant fractional orders. Finally, MATLAB R2024b simulations are run to exemplify the outcomes of this study. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos and Control of Fractional Systems)
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