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Fractal Fract
Special Issues
Applications of Fractional-Order Tools in Engineering Technology and Physical Processes
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Applications of Fractional-Order Tools in Engineering Technology and Physical Processes

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

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 3465

Special Issue Editors

Dr. Aldo Jonathan Muñoz–Vázquez

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Guest Editor
Department of Multidisciplinay Engineering, Texas A&M University, 6200 Tres Lagos Blvd, Higher Education Center at McAllen, McAllen, TX 78504, USA
Interests: fractional calculus; nonlinear systems; robotics; fuzzy logics; neural networks; control theory; integral equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Guillermo Fernández-Anaya

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Guest Editor
Department of Physics and Mathematics, Universidad Iberoamericana, Ciudad de México 01219, Mexico
Interests: fractional calculus; linear systems theory; transport phenomena; condensed matter physics; control theory; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Salah Mahmoud Boulaaras

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Guest Editor
Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia
Interests: mathematical analysis; parabolic variational inequalities; Hamilton–Jacobi–Bellman equations; numerical methods for PDEs
Special Issues, Collections and Topics in MDPI journals
Dr. Moussa Labbadi

E-Mail Website
Guest Editor
UMR 8201, CNRS, LAMIH, INSA Hauts-de-France, Université Polytechnique Hauts-de-France, F-59313 Valenciennes, France
Interests: control theory; robot motion; fractional-order control; autonomous aerial vehicles; electrical control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus has emerged as a viable tool for modeling and understanding a larger class of physical systems and engineering processes. On the one hand, fractional-order operators allow memory properties to be accounted for when studying a broader class of phenomena on a deeper level. On the other hand, these inherent properties of fractional-order systems result of interest for the design of advanced control methodologies, with greater flexibility and precision.

Fractional-order techniques can also be regarded as extensions of conventional integer-order tools, with local memory properties. For that reason, additional generalizations are currently under active research, as their implementations in the control loops are necessary to improve the controlled system response. Among these techniques, one can consider distributed- and variable-order derivatives and integrals, although additional generalizations are available in the literature, and further studies are underway.

This Special Issue aims to present outstanding and recent studies on the applications of fractional-order tools in modeling and control of physical processes and engineering systems. Manuscripts related, but not limited, to the robot control, autonomous vehicles, neural networks, fuzzy logics, advanced materials, and energy management, which use fractional-order tools, are welcome. Researchers in these mentioned fields are invited to contribute original unpublished manuscripts. Both research and review papers are welcome.

Dr. Aldo Jonathan Muñoz–Vázquez
Prof. Dr. Guillermo Fernández-Anaya
Prof. Dr. Salah Mahmoud Boulaaras
Dr. Moussa Labbadi
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

  • fractional calculus
  • robotic systems
  • fractional neural networks
  • fractional fuzzy logics
  • synchronization of fractional systems
  • fractional PID
  • fractional sliding mode control

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Published Papers (2 papers)

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14 pages, 482 KiB  
Article
Novel GPID: Grünwald–Letnikov Fractional PID for Enhanced Adaptive Cruise Control
by Diaa Eldin Elgezouli, Hassan Eltayeb and Mohamed A. Abdoon
Fractal Fract. 2024, 8(12), 751; https://doi.org/10.3390/fractalfract8120751 - 20 Dec 2024
Cited by 2 | Viewed by 795
Abstract
This study demonstrates that the Grünwald–Letnikov fractional proportional–integral–derivative (GPID) controller outperforms traditional PID controllers in adaptive cruise control systems, while conventional PID controllers struggle with nonlinearities, dynamic uncertainties, and stability, the GPID enhances robustness and provides more precise control across various driving conditions. [...] Read more.
This study demonstrates that the Grünwald–Letnikov fractional proportional–integral–derivative (GPID) controller outperforms traditional PID controllers in adaptive cruise control systems, while conventional PID controllers struggle with nonlinearities, dynamic uncertainties, and stability, the GPID enhances robustness and provides more precise control across various driving conditions. Simulation results show that the GPID improves the accuracy, reducing errors better than the PID controller. Additionally, the GPID maintains a more consistent speed and reaches the target speed faster, demonstrating superior speed control. The GPID’s performance across different fractional orders highlights its adaptability to changing road conditions, which is crucial for ensuring safety and comfort. By leveraging fractional calculus, the GPID also improves acceleration and deceleration profiles. These findings emphasize the GPID’s potential to revolutionize adaptive cruise control, significantly enhancing driving performance and comfort. Numerical results obtained in α=0.99 from the GPID controller have shown better accuracy and speed consistency, adapting to road conditions for improved safety and comfort. The GPID also demonstrated faster stabilization of speed at 60 km/h with smaller errors and reduced the error to 0.59 km/h at 50 s compared to 0.78 km/h for the PID. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Tools in Engineering Technology and Physical Processes)
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16 pages, 4245 KiB  
Article
Fixed-Time Fractional-Order Sliding Mode Control for UAVs under External Disturbances
by Abdellah Benaddy, Moussa Labbadi, Kamal Elyaalaoui and Mostafa Bouzi
Fractal Fract. 2023, 7(11), 775; https://doi.org/10.3390/fractalfract7110775 - 25 Oct 2023
Cited by 7 | Viewed by 1619
Abstract
The present paper investigates a fixed-time tracking control with fractional-order dynamics for a quadrotor subjected to external disturbances. After giving the formulation problem of a quadrotor system with six subsystems like a second-order system, a fractional-order sliding manifold is then designed to achieve [...] Read more.
The present paper investigates a fixed-time tracking control with fractional-order dynamics for a quadrotor subjected to external disturbances. After giving the formulation problem of a quadrotor system with six subsystems like a second-order system, a fractional-order sliding manifold is then designed to achieve a fixed-time convergence of the state variables. In order to cope with the upper bound of the disturbances, a switching fixed-time controller is added to the equivalent control law. Based on the switching law, fixed-time stability is ensured. All analysis and stability are proved using the Lyapunov approach. Finally, the higher performance of the proposed controller fixed-time fractional-order sliding mode control (FTFOSMC) is successfully compared to the two existing techniques through numerical simulations. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Tools in Engineering Technology and Physical Processes)
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