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Axioms
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Fractional Calculus and Applied Analysis, 2nd Edition
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Fractional Calculus and Applied Analysis, 2nd Edition

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

Deadline for manuscript submissions: 28 May 2025 | Viewed by 840

Special Issue Editor

Dr. Trushit Patel

E-Mail Website
Guest Editor
Department of General Studies, University of the People, Pasadena, CA 91101, USA
Interests: fractional differential equations; heat and mass transfer; fractional partial derivative equations; fractional physical equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to announce this Special Issue on “Fractional Calculus and Applied Analysis (FCA)” in the specialized international journal of Axioms, which invites submissions on real-world applications of mathematical analysis, both at the level of its applications and the theoretical level. In essence, fractional calculus theory is a mathematical analysis tool applied to studying integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. That is why applying fractional calculus theory has become a focus of international academic research.

The prominent members of the Editorial Board and the expertise of invited external reviewers ensure the high standards of its content. Since its inception, the journal has always aspired to be the most prestigious and suitable forum for publishing high-quality original results and surveys on special topics such as physics, biology, chemistry, heat transfer, fluid mechanics, signal processing, viscoelasticity, dynamical systems, or entropy theory, as well as for the exchange of ideas and discussion of open problems. 

Dr. Trushit Patel
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 calculus
  • multivariable fractional calculus
  • fractional integral and derivatives
  • fractional ordinary and partial differential equations
  • problems of mathematical physics
  • control theory
  • fractional stochastic processes

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Related Special Issue

Published Papers (2 papers)

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Research

15 pages, 427 KiB  
Article
Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique
by Mohammed Boukedroun, Souad Ayadi, Fouzia Chita, Meltem Erden Ege, Ozgur Ege and Rajagopalan Ramaswamy
Axioms 2025, 14(4), 233; https://doi.org/10.3390/axioms14040233 - 21 Mar 2025
Viewed by 317
Abstract
The primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditions. Our proposed approach, the Multistage Telescoping Decomposition Elzaki Method (MTDEM), [...] Read more.
The primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditions. Our proposed approach, the Multistage Telescoping Decomposition Elzaki Method (MTDEM), integrates the advantages of the Elzaki transform with the Multistage Telescoping Decomposition Method (MTDM), significantly enhancing the efficiency of the solution process and improving the convergence rate. Additionally, it simplifies computational operations and reduces the computational complexity associated with solving these nonlinear systems. A comprehensive comparison is conducted to highlight the accuracy and computational advantages of our proposed method compared to existing techniques, including the exact solution and the Telescoping Decomposition Method (TDM), through numerical examples that demonstrate the effectiveness of the proposed approach. The flexibility of the MTDEM allows for its application in a wide range of nonlinear SFDEs, making it a valuable tool in various scientific and engineering fields. These systems are widely used in modeling numerous physical, biological, and economic phenomena, such as the dynamics of electrical systems, heat transfer, and population growth models, underscoring the importance of developing accurate and efficient computational methods for their solutions. Through this study, we present a novel contribution to enhancing numerical and analytical techniques, paving the way for broader applications in multiple domains that require precise and reliable solutions for complex fractional systems. Full article
(This article belongs to the Special Issue Fractional Calculus and Applied Analysis, 2nd Edition)
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19 pages, 314 KiB  
Article
Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces
by Faryal Abdullah Al-Adsani and Ahmed Gamal Ibrahim
Axioms 2025, 14(4), 230; https://doi.org/10.3390/axioms14040230 - 21 Mar 2025
Viewed by 279
Abstract
This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a C0-semigroup or a [...] Read more.
This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a C0-semigroup or a sectorial operator and the nonlinear part is a multi-valued function with convex or nonconvex values. We provide a definition of the mild solutions, and then, by using appropriate fixed-point theorems for multi-valued functions and the properties of both the conformable derivative and the measure of noncompactness, we achieve our findings. We did not assume that the semigroup generated by the linear part is compact, and this makes our work novel and interesting. We give examples of the application of our theoretical results. Full article
(This article belongs to the Special Issue Fractional Calculus and Applied Analysis, 2nd Edition)
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