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Axioms
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Current Perspectives in Fractional Calculus: Theory, Methods, and Applications
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Current Perspectives in Fractional Calculus: Theory, Methods, and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 20 December 2024 | Viewed by 1353

Special Issue Editor

Dr. José Villa-Morales

E-Mail Website
Guest Editor
Department of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes 20100, Mexico
Interests: integral equations; partial differential equations; stochastic differential equations; fractional calculus

Special Issue Information

Dear Colleagues,

Fractional calculus has emerged as an area of great interest across various fields due to its ability to model complex phenomena with memory and long-term dependencies. It has found applications in a wide range of disciplines, including engineering, physics, economics, and more recently, life sciences. The versatility of fractional calculus has rendered it an invaluable tool for understanding and addressing problems that cannot be adequately modeled using traditional methods.

This Special Issue aims to provide a platform for sharing the latest advancements in the theory, methods, and applications of fractional calculus, encompassing a wide range of topics including theoretical research, analytical developments, numerical and computational methods, as well as practical applications across diverse fields.

The articles featured in this Special Issue will explore new topics and techniques in fractional calculus, considering solution methods for fractional equations, applications in dynamical systems, and control and optimization, among others. Additionally, special emphasis will be placed on recent advances in the interdisciplinary application of fractional calculus, highlighting its potential to address complex challenges in areas such as engineering, applied physics, computer science, and beyond.

Dr. José Villa-Morales
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. Axioms 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 2400 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 view analysis in life sciences
  • applications of fractional calculus to biological systems
  • recent developments of fractional theory
  • fractional differential equations
  • chaos and bifurcation in fractional systems
  • analytic approaches in fractional calculus
  • computational analysis of natural systems
  • biomedical applications of fractional calculus
  • fractional molecular cellular dynamics
  • numerical methods for fractional systems

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Published Papers (2 papers)

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Research

22 pages, 351 KiB  
Article
Revised and Generalized Results of Averaging Principles for the Fractional Case
by Muhammad Imran Liaqat, Zareen A. Khan, J. Alberto Conejero and Ali Akgül
Axioms 2024, 13(11), 732; https://doi.org/10.3390/axioms13110732 - 23 Oct 2024
Viewed by 426
Abstract
The averaging principle involves approximating the original system with a simpler system whose behavior can be analyzed more easily. Recently, numerous scholars have begun exploring averaging principles for fractional stochastic differential equations. However, many previous studies incorrectly defined the standard form of these [...] Read more.
The averaging principle involves approximating the original system with a simpler system whose behavior can be analyzed more easily. Recently, numerous scholars have begun exploring averaging principles for fractional stochastic differential equations. However, many previous studies incorrectly defined the standard form of these equations by placing ε in front of the drift term and ε in front of the diffusion term. This mistake results in incorrect estimates of the convergence rate. In this research work, we explain the correct process for determining the standard form for the fractional case, and we also generalize the result of the averaging principle and the existence and uniqueness of solutions to fractional stochastic delay differential equations in two significant ways. First, we establish the result in Lp space, generalizing the case of p=2. Second, we establish the result using the Caputo–Katugampola operator, which generalizes the results of the Caputo and Caputo–Hadamard derivatives. Full article
(This article belongs to the Special Issue Current Perspectives in Fractional Calculus: Theory, Methods, and Applications)
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26 pages, 2931 KiB  
Article
Positivity-Preserving Rational Cubic Fractal Interpolation Function Together with Its Zipper Form
by Shamli Sharma, Kuldip Katiyar, Gadug Sudhamsu, Manjinder Kaur Wratch and Rohit Salgotra
Axioms 2024, 13(9), 584; https://doi.org/10.3390/axioms13090584 - 28 Aug 2024
Viewed by 626
Abstract
In this paper, a novel class of rational cubic fractal interpolation function (RCFIF) has been proposed, which is characterized by one shape parameter and a linear denominator. In interpolation for shape preservation, the proposed rational cubic fractal interpolation function provides a simple but [...] Read more.
In this paper, a novel class of rational cubic fractal interpolation function (RCFIF) has been proposed, which is characterized by one shape parameter and a linear denominator. In interpolation for shape preservation, the proposed rational cubic fractal interpolation function provides a simple but effective approach. The nature of shape preservation of the proposed rational cubic fractal interpolation function makes them valuable in the field of data visualization, as it is crucial to maintain the original data shape in data visualization. Furthermore, we discussed the upper bound of error and explored the mathematical framework to ensure the convergence of RCFIF. Shape parameters and scaling factors are constraints to obtain the desired shape-preserving properties. We further generalized the proposed RCFIF by introducing the concept of signature, giving its construction in the form of a zipper-rational cubic fractal interpolation function (ZRCFIF). The positivity conditions for the rational cubic fractal interpolation function and zipper-rational cubic fractal interpolation function are found, which required a detailed analysis of the conditions where constraints on shape parameters and scaling factor lead to the desired shape-preserving properties. In the field of shape preservation, the proposed rational cubic fractal interpolation function and zipper fractal interpolation function both represent significant advancement by offering a strong tool for data visualization. Full article
(This article belongs to the Special Issue Current Perspectives in Fractional Calculus: Theory, Methods, and Applications)
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