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Fractal Fract
Special Issues
Operators of Fractional Integration and Their Applications
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Operators of Fractional Integration and Their Applications

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

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 5049

Special Issue Editors

Dr. Abd-Allah Hyder

E-Mail Website
Guest Editor
1. Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
2. Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo 71524, Egypt
Interests: fractional calculus and its applications; analytical solutions for nonlinear models; analysis of integral inequalities; fractional biological models; fixed point theory; fractional optimal control
Dr. Mohamed A. Barakat

E-Mail Website
Guest Editor
1. Department of Computer Science, College of Al Wajh, University of Tabuk, Tabuk 71491, Saudi Arabia
2. Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt
Interests: fractional calculus and its applications; fixed point theory; analytical solutions for nonlinear models; analysis of integral inequalities; fractional biological models

Special Issue Information

Dear Colleagues,

Nowadays, it has been discovered that numerous types of fractional integral and derivative operators, such as those called after Riemann–Liouville, Hadamard, Weyl, Liouville–Caputo, Riesz, Grunwald–Letnikov, Erdelyi–Kober, and others, have been observed to be extremely significant and productive. This is because of their demonstrated applications in abundant and widely spread areas of the mathematical, physical, engineering, biological, statistical and chemical disciplines. Many of these fractional operators offer intriguing, potentially helpful tools for solving integral and integro-differential equations, as well as investigating optimal control the problem of fractional systems. Moreover, they also provide solutions to a variety of other issues involving special functions from applied mathematics and mathematical physics, as well as their extensions and generalizations in different directions.

On the other hand, differential and integral fractional equations have been solved successfully by calculating the fixed point for fractional integral operators. By bearing in mind that virtually many real-world problems may be transformed into problems of fractional differential and integral equations. So, we can reach a conclusion about the importance of the fractional integral operators together with fixed point theory in qualitative science and technology.

In this Special Issue, original research, expository and review articles addressing current developments in the theory fractional integrals and derivatives, as well as their applications.

Dr. Abd-Allah Hyder
Dr. Mohamed A. Barakat
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 integral operators and their applications
  • fractional ODEs and PDEs
  • fractional integro-differential equations
  • fractional epidemic models
  • fractional integrals associated with special functions from mathematical physics
  • well-posedness of fractional systems via fixed point theory and fractional integral operators
  • optimal control of fractional cooperative and non-cooperative systems

Published Papers (3 papers)

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Research

19 pages, 350 KiB  
Article
Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain
by Timilehin Gideon Shaba, Serkan Araci, Babatunde Olufemi Adebesin, Fairouz Tchier, Saira Zainab and Bilal Khan
Fractal Fract. 2023, 7(7), 506; https://doi.org/10.3390/fractalfract7070506 - 27 Jun 2023
Cited by 7 | Viewed by 1071
Abstract
In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the q-derivative operator. [...] Read more.
In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the q-derivative operator. Furthermore, we find the initial Taylor–Maclaurin coefficients for these newly defined function classes of analytic and bi-univalent functions. We also show that these bounds are sharp. The sharp second Hankel determinant is also given for this newly defined function class. Full article
(This article belongs to the Special Issue Operators of Fractional Integration and Their Applications)
16 pages, 1764 KiB  
Article
A New Class of Generalized Fractal and Fractal-Fractional Derivatives with Non-Singular Kernels
by Khalid Hattaf
Fractal Fract. 2023, 7(5), 395; https://doi.org/10.3390/fractalfract7050395 - 12 May 2023
Cited by 17 | Viewed by 2349
Abstract
The present paper introduces a new class of generalized differential and integral operators. This class includes and generalizes a large number of definitions of fractal-fractional derivatives and integral operators used to model the complex dynamics of many natural and physical phenomena found in [...] Read more.
The present paper introduces a new class of generalized differential and integral operators. This class includes and generalizes a large number of definitions of fractal-fractional derivatives and integral operators used to model the complex dynamics of many natural and physical phenomena found in diverse fields of science and engineering. Some properties of the newly introduced class are rigorously established. As applications of this new class, two illustrative examples are presented, one for a simple problem and the other for a nonlinear problem modeling the dynamical behavior of a chaotic system. Full article
(This article belongs to the Special Issue Operators of Fractional Integration and Their Applications)
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14 pages, 333 KiB  
Article
Analysis of the Fractional HIV Model under Proportional Hadamard-Caputo Operators
by Areej A. Almoneef, Mohamed A. Barakat and Abd-Allah Hyder
Fractal Fract. 2023, 7(3), 220; https://doi.org/10.3390/fractalfract7030220 - 28 Feb 2023
Cited by 4 | Viewed by 925
Abstract
Modeling human immunodeficiency virus (HIV) via fractional operators has several benefits over the classical integer-order HIV model. The reason is that the fractional HIV model relies not only on the recent status but also on the former conduct of the model. Thus, we [...] Read more.
Modeling human immunodeficiency virus (HIV) via fractional operators has several benefits over the classical integer-order HIV model. The reason is that the fractional HIV model relies not only on the recent status but also on the former conduct of the model. Thus, we are motivated to introduce and analyze a new fractional HIV model. This article focuses on a novel fractional HIV model under the proportional Hadamard-Caputo fractional operators. The study of this model involves the existence and uniqueness (EU) of its solution and the stability examination. We employ Leray–Schauder nonlinear alternative (L-SNLA) and Banach’s fixed point theorems to analyze the EU results. In addition, for this provided model, we develop several forms of Ulam’s stability findings. As a special case of our results, we give and analyze a new fractional HIV model with Hadamard-Caputo operators. Moreover, by appropriate choice of the fractional parameters, the obtained outcomes are valid for analysis of the fractional HIV models formed by several fractional operators defined in the past literature. Full article
(This article belongs to the Special Issue Operators of Fractional Integration and Their Applications)
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