Fractional Calculus and Mathematical Applications, 2nd Edition

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 4001

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Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Av. Libertad 5450, Corrientes 3400, Argentina
Interests: fractional calculus; generalized calculus; integral inequalities; qualitative theory of ordinary differential equations
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Special Issue Information

Dear Colleagues,

We are delighted to announce the second volume of our Special Issue on "Fractional Calculus and Mathematical Applications". Building upon the success of the first volume, we aim to continue exploring the fascinating realm of fractional calculus and its diverse applications.

Fractional calculus possesses a unique dual nature. On the one hand, it shares a long history with ordinary (integer) calculus. On the other hand, over the past four decades, it has witnessed exponential growth in its applications across various fields and diverse topics. This interdisciplinary collaboration has resulted in an ever-increasing number of researchers and publications. From biological models to integral inequalities, from systems with delay to neutrals and hybrids, fractional calculus has found its utility and effectiveness in addressing a wide range of theoretical investigations and practical problems.

Our focus extends beyond traditional integral operators of the Riemann–Liouville type. We embrace the use of differential operators such as Caputo or Riemann–Liouville and their generalizations, allowing for the incorporation of a rich variety of mathematical tools. These tools have been extensively tested and have proven effective in tackling an array of challenging problems.

As a consequence, this vibrant field continues to produce new and exciting results. These advancements involve increasingly generalized integral operators and novel types of fractional differentials, expanding the horizons of fractional calculus to unprecedented boundaries.

We cordially invite researchers from all mathematical disciplines to contribute their latest findings and insights to this Special Issue. We aim to push the boundaries of knowledge and explore the uncharted territories of fractional calculus.

Prof. Dr. Juan Eduardo Nápoles Valdes
Guest Editor

Manuscript Submission Information

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Keywords

  • fractional calculus
  • q-calculus
  • fractional integral and differential operators
  • fractional differential equation
  • fractional integral equation
  • integral inequalities

Related Special Issue

Published Papers (6 papers)

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Research

18 pages, 799 KiB  
Article
Refinements and Applications of Hermite–Hadamard-Type Inequalities Using Hadamard Fractional Integral Operators and GA-Convexity
by Muhammad Amer Latif
Mathematics 2024, 12(3), 442; https://doi.org/10.3390/math12030442 - 30 Jan 2024
Viewed by 464
Abstract
In this paper, several applications of the Hermite–Hadamard inequality for fractional integrals using GA-convexity are discussed, including some new refinements and similar extensions, as well as several applications in the Gamma and incomplete Gamma functions. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
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11 pages, 779 KiB  
Article
The Fractional Dunkl Laplacian: Definition and Harmonization via the Mellin Transform
by Fethi Bouzeffour
Mathematics 2023, 11(22), 4668; https://doi.org/10.3390/math11224668 - 16 Nov 2023
Viewed by 604
Abstract
In this paper, we extend the scope of the Tate and Ormerod Lemmas to the Dunkl setting, revealing a profound interconnection that intricately links the Dunkl transform and the Mellin transform. This illumination underscores the pivotal significance of the Mellin integral transform in [...] Read more.
In this paper, we extend the scope of the Tate and Ormerod Lemmas to the Dunkl setting, revealing a profound interconnection that intricately links the Dunkl transform and the Mellin transform. This illumination underscores the pivotal significance of the Mellin integral transform in the realm of fractional calculus associated with differential-difference operators. Our primary focus centers on the Dunkl–Laplace operator, which serves as a prototype of a differential-difference second-order operator within an unbounded domain. Following influential research by Pagnini and Runfola, we embark on an innovative exploration employing Bochner subordination approaches tailored for the fractional Dunkl Laplacian (FDL). Notably, the Mellin transform emerges as a robust and enlightening tool, particularly in its application to the FDL. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
13 pages, 328 KiB  
Article
Variable-Order Fractional Scale Calculus
by Duarte Valério and Manuel D. Ortigueira
Mathematics 2023, 11(21), 4549; https://doi.org/10.3390/math11214549 - 04 Nov 2023
Cited by 1 | Viewed by 669
Abstract
General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average [...] Read more.
General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
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18 pages, 318 KiB  
Article
(ω,ρ)-BVP Solution of Impulsive Hadamard Fractional Differential Equations
by Ahmad Al-Omari and Hanan Al-Saadi
Mathematics 2023, 11(20), 4370; https://doi.org/10.3390/math11204370 - 20 Oct 2023
Cited by 1 | Viewed by 593
Abstract
The purpose of this research is to examine the uniqueness and existence of the (ω,ρ)-BVP solution for a particular solution to a class of Hadamard fractional differential equations with impulsive boundary value requirements on Banach spaces. The notion [...] Read more.
The purpose of this research is to examine the uniqueness and existence of the (ω,ρ)-BVP solution for a particular solution to a class of Hadamard fractional differential equations with impulsive boundary value requirements on Banach spaces. The notion of Banach contraction and Schaefer’s theorem are used to prove the study’s key findings. In addition, we offer the prerequisites for the set of solutions to the investigated boundary value with impulsive fractional differential issue to be convex. To enhance the comprehension and practical application of our findings, we offer two illustrative examples at the end of the paper to show how the results can be applied. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
9 pages, 260 KiB  
Article
On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk
by Astamur Bagapsh and Alexandre Soldatov
Mathematics 2023, 11(20), 4360; https://doi.org/10.3390/math11204360 - 20 Oct 2023
Viewed by 564
Abstract
The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk are given. In [...] Read more.
The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk are given. In addition, an iterative method for solving this problem for systems with respect to two unknown functions is described, and an integral representation of the Poisson type is obtained by applying this method. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
14 pages, 287 KiB  
Article
(ω,ρ)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces
by Michal Fečkan, Marko Kostić and Daniel Velinov
Mathematics 2023, 11(14), 3086; https://doi.org/10.3390/math11143086 - 13 Jul 2023
Cited by 2 | Viewed by 663
Abstract
The paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as (ω,ρ)-BVP solution. The proof of the [...] Read more.
The paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as (ω,ρ)-BVP solution. The proof of the main results of this study involves the application of the Banach contraction mapping principle and Schaefer’s fixed point theorem. Furthermore, we provide the necessary conditions for the convexity of the set of solutions of the analyzed impulsive fractional differential boundary value problem. To enhance the comprehension and practical application of our findings, we conclude the paper by presenting two illustrative examples that demonstrate the applicability of the obtained results. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
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