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Fractal Fract
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Advances in Dynamics and Control of Fractional-Order Systems
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Advances in Dynamics and Control of Fractional-Order Systems

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

Deadline for manuscript submissions: 31 July 2026 | Viewed by 1768

Special Issue Editor

Dr. Ruihong Li

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xidian University, Xi'an, China
Interests: fractional-order system; bifurcation and chaos; parameter identification; control and synchronization

Special Issue Information

Dear Colleagues,

Fractional-order calculus, which involves memory and genetic characteristics, can be viewed as the generalization of its traditional integer-order counterpart. Due to its special properties, considerable physical systems can be modeled by fractional-order calculus, such as viscoelastic systems, polymeric chemistry systems, biomedical systems, circuit systems, and electrode processes. With the deepening of research problems, models, such as fractional-order nonlinear systems, fractional-order delay systems, fractional-order network systems, and stochastic fractional-order systems, have emerged. It is worth noting that fractional-order systems can exhibit rich and complex dynamical behaviors, which are currently being explored in numerous fields of science and engineering. In recent years, many researchers have worked on the theory of fractional-order control. Compared with integer-order control, fractional-order control retains several advantages. One is that it is more suitable for flexible structures, especially those with viscoelastic properties. Another reason is that it can effectively improve the adaptability and robustness of the system, making it suitable for the control requirements of various complex systems.

The focus of this Special Issue is to continue to advance research on topics relating to the modeling, dynamic analysis, control, and application of fractional-order systems. Topics that are invited for submission include (but are not limited to) the following:

  • Resonance, bifurcation, and chaotic behavior in fractional-order systems;
  • Resonance analysis and stability analysis of fractional-order systems;
  • Nonlinear dynamics of fractional-order systems;
  • Uncertain fractional-order system;
  • Adaptive control of fractional-order systems;
  • Backstepping control of fractional-order systems;
  • Model predictive control for fractional-order systems;
  • Intelligent control of fractional-order systems;
  • Fractional-order optimization;
  • System identification for fractional-order models.

Dr. Ruihong Li
Guest Editor

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

  • complex dynamical behaviors
  • bifurcation analysis
  • stability analysis
  • resonance analysis
  • chaos synchronization
  • control strategies
  • system identification

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

Published Papers (4 papers)

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Research

24 pages, 6140 KB  
Article
Stabilization of DC Microgrids Using Frequency-Decomposed Fractional-Order Control and Hybrid Energy Storage
by Sherif A. Zaid, Hani Albalawi, Hazem M. El-Hageen, Abdul Wadood and Abualkasim Bakeer
Fractal Fract. 2025, 9(10), 670; https://doi.org/10.3390/fractalfract9100670 - 17 Oct 2025
Viewed by 385
Abstract
In DC microgrids, the combination of pulsed loads and renewable energy sources significantly impairs system stability, especially in highly dynamic operating environments. The resilience and reaction time of conventional proportional–integral (PI) controllers are often inadequate when managing the nonlinear dynamics of hybrid energy [...] Read more.
In DC microgrids, the combination of pulsed loads and renewable energy sources significantly impairs system stability, especially in highly dynamic operating environments. The resilience and reaction time of conventional proportional–integral (PI) controllers are often inadequate when managing the nonlinear dynamics of hybrid energy storage systems. This research suggests a frequency-decomposed fractional-order control strategy for stabilizing DC microgrids with solar, batteries, and supercapacitors. The control architecture divides system disturbances into low- and high-frequency components, assigning high-frequency compensation to the ultracapacitor (UC) and low-frequency regulation to the battery, while a fractional-order controller (FOC) enhances dynamic responsiveness and stability margins. The proposed approach is implemented and assessed in MATLAB/Simulink (version R2023a) using comparison simulations against a conventional PI-based control scheme under scenarios like pulsed load disturbances and fluctuations in renewable generation. Grey Wolf Optimizer (GWO), a metaheuristic optimization procedure, has been used to tune the parameters of the FOPI controller. The obtained results using the same conditions were compared using an optimal fractional-order PI controller (FOPI) and a conventional PI controller. The microgrid with the best FOPI controller was found to perform better than the one with the PI controller. Consequently, the objective function is reduced by 80% with the proposed optimal FOPI controller. The findings demonstrate that the proposed method significantly enhances DC bus voltage management, reduces overshoot and settling time, and lessens battery stress by effectively coordinating power sharing with the supercapacitor. Also, the robustness of the proposed controller against parameters variations has been proven. Full article
(This article belongs to the Special Issue Advances in Dynamics and Control of Fractional-Order Systems)
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24 pages, 1878 KB  
Article
Advancements in Sustainable Mobility: Fractional-Order FOC of IM in an Electric Vehicle Powered by an Autonomous PV Battery System
by Fatma Ben Salem, Jaouhar Mouine and Nabil Derbel
Fractal Fract. 2025, 9(10), 661; https://doi.org/10.3390/fractalfract9100661 - 14 Oct 2025
Viewed by 349
Abstract
This paper presents a novel fractional-order field-oriented control (FO-FOC) strategy for induction motor drives in electric vehicles (EVs) powered by an autonomous photovoltaic (PV) battery energy system. The proposed control approach integrates a fractional-order sliding mode controller (FO-SMC) into the conventional FOC framework [...] Read more.
This paper presents a novel fractional-order field-oriented control (FO-FOC) strategy for induction motor drives in electric vehicles (EVs) powered by an autonomous photovoltaic (PV) battery energy system. The proposed control approach integrates a fractional-order sliding mode controller (FO-SMC) into the conventional FOC framework to enhance dynamic performance, improve robustness, and reduce sensitivity to parameter variations. The originality of this work lies in the combined use of fractional-order control and real-time adaptive parameter updating, applied within a PV battery-powered EV platform. This dual-layer control structure allows the system to effectively reject disturbances, maintain torque and flux tracking, and mitigate the effects of component aging or thermal drift. Furthermore, to address the chattering phenomenon typically associated with sliding mode control, a continuous saturation function was employed, resulting in smoother voltage and current responses more suitable for real-time implementation. Extensive simulation studies were conducted under ideal conditions, with parameter mismatch, and with the proposed adaptive update laws. Results confirmed the superiority of the FO-based approach over classical integer-order designs in terms of speed tracking, flux regulation, torque ripple reduction, and system robustness. The proposed methodology offers a promising solution for next-generation sustainable mobility systems requiring high-performance, energy-efficient, and fault-tolerant electric drives. Full article
(This article belongs to the Special Issue Advances in Dynamics and Control of Fractional-Order Systems)
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24 pages, 9636 KB  
Article
Finite-Time Modified Function Projective Synchronization Between Different Fractional-Order Chaotic Systems Based on RBF Neural Network and Its Application to Image Encryption
by Ruihong Li, Huan Wang and Dongmei Huang
Fractal Fract. 2025, 9(10), 659; https://doi.org/10.3390/fractalfract9100659 - 13 Oct 2025
Viewed by 243
Abstract
This paper innovatively achieves finite-time modified function projection synchronization (MFPS) for different fractional-order chaotic systems. By leveraging the advantages of radial basis function (RBF) neural networks in nonlinear approximation, this paper proposes a novel fractional-order sliding-mode controller. It is designed to address the [...] Read more.
This paper innovatively achieves finite-time modified function projection synchronization (MFPS) for different fractional-order chaotic systems. By leveraging the advantages of radial basis function (RBF) neural networks in nonlinear approximation, this paper proposes a novel fractional-order sliding-mode controller. It is designed to address the issues of system model uncertainty and external disturbances. Based on Lyapunov stability theory, it has been demonstrated that the error trajectory can converge to the equilibrium point along the sliding surface within a finite time. Subsequently, the finite-time MFPS of the fractional-order hyperchaotic Chen system and fractional-order chaotic entanglement system are realized under conditions of periodic and noise disturbances, respectively. The effects of the neural network parameters on the performance of the MFPS are then analyzed in depth. Finally, a color image encryption scheme is presented integrating the above MFPS method and exclusive-or operation, and its effectiveness and security are illustrated through numerical simulation and statistical analysis. In the future, we will further explore the application of fractional-order chaotic system MFPS in other fields, providing new theoretical support for interdisciplinary research. Full article
(This article belongs to the Special Issue Advances in Dynamics and Control of Fractional-Order Systems)
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18 pages, 1082 KB  
Article
Dynamics in a Fractional-Order Four-Species Food Web System with Top Predator and Delays
by Xiao Tang and Ahmadjan Muhammadhaji
Fractal Fract. 2025, 9(10), 650; https://doi.org/10.3390/fractalfract9100650 - 8 Oct 2025
Viewed by 340
Abstract
The predator–prey model is a fundamental mathematical tool in ecology used to understand the dynamic relationship between predator and prey populations. This study develops a fractional-order delayed dynamical model for a four-species food web, which includes an intermediate predator feeding on two prey [...] Read more.
The predator–prey model is a fundamental mathematical tool in ecology used to understand the dynamic relationship between predator and prey populations. This study develops a fractional-order delayed dynamical model for a four-species food web, which includes an intermediate predator feeding on two prey species and a top predator preying on all three species. The boundedness of the system’s solutions is first rigorously established using the Laplace transform method. Next, a nonlinear dynamical analysis is performed to determine the existence conditions and local stability of both the trivial and positive equilibrium points. In particular, by treating the time delay as a bifurcation control parameter, explicit criteria for the onset of Hopf bifurcation are derived. Theoretically, when the delay magnitude exceeds a critical threshold, the system loses stability and exhibits sustained oscillatory behavior. Finally, systematic numerical simulations are performed under specific parameter settings. The effects of varying fractional orders and delay magnitudes on the system’s dynamics are quantitatively explored, and the results show strong agreement with the theoretical predictions. Full article
(This article belongs to the Special Issue Advances in Dynamics and Control of Fractional-Order Systems)
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