Fractional Calculus: Advances and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 1235

Special Issue Editors


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Department of Electrical Engineering, Engineering Division Campus Irapuato-Salamanca, University of Guanajuato, Salamanca 36885, Mexico
Interests: fractional calculus; fractional calculation; fractional differential equations; fractional derivative; supersymmetric cosmology

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Guest Editor
Instituto de Engenharia Mecânica (IDMEC), Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Interests: fractional calculus; fractional control; wave energy conversion; data mining
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Special Issue Information

Dear Colleagues, 

In recent years, fractional calculus (FC) has been shown to be more accurate for describing real processes than the ordinary calculus. FC is the natural generalization of the ordinary calculus, and fractional derivatives are defined by integrals, making them non-local. This means that the fractional time derivative simulates memory effects, and the spatial fractional derivative describes non-local spatial effects. There are several results demonstrating the remarkable advantages of fractional calculus over the ordinary calculus, e.g., the new theory of capacitors, anomalous diffusion, memory mechanisms, bioengineering, electromagnetism, fractional electrical circuits, fractional-order control, and nanotechnology, to mention a few. 

The Special Issue “Fractional Calculus: Advances and Applications” aims to collate original articles with various contributions, such as new methods for solving fractional differential equations and applications in all areas of science and engineering, such as fractional control, electromagnetic theory, bioengineering, and mechanics. Studies on fractional cosmology are welcome.

Prof. Dr. Juan J. Rosales-García
Dr. Duarte Valério
Guest Editors

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Keywords

  • methods for solving fractional differential equations
  • new theory of capacitors
  • fractional electromagnetic theory
  • fractional bioengineering
  • fractional cosmology
  • non-ordinary mechanics
  • signal and image processing
  • fractional biomedical signals and images
  • fractional circuit theory

Published Papers (2 papers)

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31 pages, 2716 KiB  
Article
Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects
by Safoura Rezaei Aderyani, Reza Saadati, Donal O’Regan and Fehaid Salem Alshammari
Mathematics 2024, 12(6), 904; https://doi.org/10.3390/math12060904 - 19 Mar 2024
Viewed by 377
Abstract
We apply known special functions from the literature (and these include the Fox Hfunction, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the Gfunction, the Fox–Wright function and the Meijer Gfunction) and [...] Read more.
We apply known special functions from the literature (and these include the Fox Hfunction, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the Gfunction, the Fox–Wright function and the Meijer Gfunction) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory. Full article
(This article belongs to the Special Issue Fractional Calculus: Advances and Applications)
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23 pages, 548 KiB  
Article
Best Decision-Making on the Stability of the Smoke Epidemic Model via Z-Numbers and Aggregate Special Maps
by Donal O’Regan, Safoura Rezaei Aderyani and Reza Saadati
Mathematics 2024, 12(6), 871; https://doi.org/10.3390/math12060871 - 15 Mar 2024
Viewed by 426
Abstract
The present paper considers a fractional-order smoke epidemic model. We apply fuzzy systems and probability theory to make the best decision on the stability of the smoking epidemic model by using a new class of controllers powered by special functions to effectively generalize [...] Read more.
The present paper considers a fractional-order smoke epidemic model. We apply fuzzy systems and probability theory to make the best decision on the stability of the smoking epidemic model by using a new class of controllers powered by special functions to effectively generalize Ulam-type stability problems. Evaluation of optimal controllability and maximal stability is the new issue. This different concept of stability not only covers the old concepts but also investigates the optimization of the problem. Finally, we apply a new optimal method for the governing model with the Atangana–Baleanu–Caputo fractional derivative to obtain stability results in Banach spaces. Full article
(This article belongs to the Special Issue Fractional Calculus: Advances and Applications)
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