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Fractal Fract
Special Issues
Operators of Fractional Calculus and Their Multi-Disciplinary Applications
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Special Issue "Operators of Fractional Calculus and Their Multi-Disciplinary 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: 15 December 2021.

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava
grade E-Mail Website
SciProfiles
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modelling and optimization
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Current widespread interest in various families of fractional-order integral and derivative operators, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdélyi–Kober, Liouville–Caputo, and so on, have stemmed essentially from their demonstrated applications in numerous diverse areas of the mathematical, physical, chemical, engineering, and statistical sciences. These fractional-order operators provide interesting and potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations, the fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, applicable analysis and applied mathematics, as well as their extensions and generalizations in one, two and more variables.

In this Special Issue, we invite and welcome review, expository, and original research articles dealing with recent advances in the theory of integrals and derivatives of fractional order and their multidisciplinary applications.

Prof. Dr. Hari Mohan Srivastava
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 papers will be 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 quarterly 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 1600 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

  • operators of fractional integrals and fractional derivatives and their applications
  • chaos and dynamical systems based upon fractional calculus
  • fractional-order ODEs and PDEs
  • fractional-order differintegral and integro-differential equations
  • integrals and derivatives of fractional order associated with special functions of mathematical physics and applied mathematics
  • identities and inequalities involving fractional-order integrals and fractional-order derivatives

Published Papers (3 papers)

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Research

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Article
Uniqueness of Solutions of the Generalized Abel Integral Equations in Banach Spaces
by
Chenkuan Li
and
Hari M. Srivastava
Fractal Fract. 2021, 5(3), 105; https://doi.org/10.3390/fractalfract5030105 - 31 Aug 2021
Viewed by 195
Abstract
This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multivariate Mittag–Leffler function. We also present some [...] Read more.
This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multivariate Mittag–Leffler function. We also present some examples for the illustration of our main theorems. Full article
(This article belongs to the Special Issue Operators of Fractional Calculus and Their Multi-Disciplinary Applications)
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Article
On the Nonlinear Integro-Differential Equations
by
Chenkuan Li
and
Joshua Beaudin
Fractal Fract. 2021, 5(3), 82; https://doi.org/10.3390/fractalfract5030082 - 30 Jul 2021
Viewed by 287
Abstract
The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s [...] Read more.
The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s contractive principle, the multivariate Mittag–Leffler function and Babenko’s approach. We also provide a few examples to demonstrate the use of our main theorems by convolutions and the gamma function. Full article
(This article belongs to the Special Issue Operators of Fractional Calculus and Their Multi-Disciplinary Applications)
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Article
On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus
by
Gul Sana
,
Pshtiwan Othman Mohammed
,
Dong Yun Shin
,
Muhmmad Aslam Noor
and
Mohammad Salem Oudat
Fractal Fract. 2021, 5(3), 60; https://doi.org/10.3390/fractalfract5030060 - 25 Jun 2021
Viewed by 471
Abstract
Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q [...] Read more.
Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q-iterative methods by using the q-analogue of the Taylor’s series and the coupled system technique. In the domain of q-calculus, we determine the convergence of our proposed q-algorithms. Numerical examples demonstrate that the new q-iterative methods can generate solutions to the nonlinear equations with acceptable accuracy. These newly established methods also exhibit predictability. Furthermore, an analogy is settled between the well known classical methods and our proposed q-Iterative methods. Full article
(This article belongs to the Special Issue Operators of Fractional Calculus and Their Multi-Disciplinary Applications)
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