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Advances in Fractional Operators and Their Applications in Physical Sciences
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Advances in Fractional Operators and Their Applications in Physical Sciences

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 6206

Special Issue Editors

Prof. Dr. Jagdev Singh

E-Mail Website
Guest Editor
Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
Interests: fractional calculus; mathematical modelling; numerical methods; special functions; applied analysis
Dr. Devendra Kumar

grade E-Mail Website
Guest Editor
Department of Mathematics, University of Rajasthan, Jaipur 302004, India
Interests: fractional calculus; fractional dynamics; special functions; mathematical modelling; fractional differential equations; analytical and numerical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue (SI) is mainly focused on addressing a broad range of fractional order operators, and their uses in different directions of physics, chemistry and engineering. In this SI, we invite and welcome review, expository and original and high quality research papers dealing with the new advances on the topics of fractional derivatives and integrals in addition to their applications in physical sciences:

Topics

  • Fractional order derivatives and integrals with their applications.
  • Fractional order dynamical processes.
  • Applications of fractional calculus in fluid mechanics.
  •  Use of fractional derivatives in quantum mechanics.
  • Application of fractional derivatives in Chaos theory.
  • Fractional differential equations arising in biological systems.
  • Fractional differential equations arising in economics.
  • Analytical and numerical techniques for fractional order differential equations.
  • Fractional optimal control problems.
  • Fractional complex systems.

The selection process will be based on the reviewer’s evaluations of the papers. Possible authors should kindly submit an electronic copy of the complete manuscript via the manuscript tracking system.

Prof. Dr. Jagdev Singh
Dr. Devendra Kumar
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Published Papers (5 papers)

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Research

14 pages, 568 KiB  
Article
Novel Kinds of Fractional λ–Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral
by Mohammed Z. Alqarni and Mohamed Abdalla
Mathematics 2023, 11(19), 4217; https://doi.org/10.3390/math11194217 - 9 Oct 2023
Cited by 1 | Viewed by 689
Abstract
In recent years, fractional kinetic equations (FKEs) involving various special functions have been widely used to describe and solve significant problems in control theory, biology, physics, image processing, engineering, astrophysics, and many others. This current work proposes a new solution to fractional [...] Read more.
In recent years, fractional kinetic equations (FKEs) involving various special functions have been widely used to describe and solve significant problems in control theory, biology, physics, image processing, engineering, astrophysics, and many others. This current work proposes a new solution to fractional λ−kinetic equations based on generalized degenerate hypergeometric functions (GDHFs), which has the potential to be applied to calculate changes in the chemical composition of stars such as the sun. Furthermore, this expanded form can also help to solve various problems with phenomena in physics, such as fractional statistical mechanics, anomalous diffusion, and fractional quantum mechanics. Moreover, some of the well-known outcomes are just special cases of this class of pathway-type solutions involving GDHFs, with greater accuracy, while providing an easily calculable solution. Additionally, numerical graphs of these analytical solutions, using MATLAB Software (latest version 2023b), are also considered. Full article
(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)
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11 pages, 272 KiB  
Article
On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities
by Juan Gabriel Galeano Delgado, Juan Eduardo Nápoles Valdés and Edgardo Enrique Pérez Reyes
Mathematics 2023, 11(16), 3565; https://doi.org/10.3390/math11163565 - 17 Aug 2023
Cited by 1 | Viewed by 765
Abstract
In this paper, we present a general formulation of the Riemann–Liouville fractional operator with generalized kernels. Many of the known operators are shown to be particular cases of the one we present. In this new framework, we prove several known integral inequalities in [...] Read more.
In this paper, we present a general formulation of the Riemann–Liouville fractional operator with generalized kernels. Many of the known operators are shown to be particular cases of the one we present. In this new framework, we prove several known integral inequalities in the literature. Full article
(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)
11 pages, 414 KiB  
Article
A Proposed Application of Fractional Calculus on Time Dilation in Special Theory of Relativity
by Ebrahem A. Algehyne, Musaad S. Aldhabani, Mounirah Areshi, Essam R. El-Zahar, Abdelhalim Ebaid and Hind K. Al-Jeaid
Mathematics 2023, 11(15), 3343; https://doi.org/10.3390/math11153343 - 30 Jul 2023
Cited by 4 | Viewed by 1140
Abstract
Time dilation (TD) is a principal concept in the special theory of relativity (STR). The Einstein TD formula is the relation between the proper time t0 measured in a moving frame of reference with velocity v and the dilated time t measured [...] Read more.
Time dilation (TD) is a principal concept in the special theory of relativity (STR). The Einstein TD formula is the relation between the proper time t0 measured in a moving frame of reference with velocity v and the dilated time t measured by a stationary observer. In this paper, an integral approach is firstly presented to rededuce the Einstein TD formula. Then, the concept of TD is introduced and examined in view of the fractional calculus (FC) by means of the Caputo fractional derivative definition (CFD). In contrast to the explicit standard TD formula, it is found that the fractional TD (FTD) is governed by a transcendental equation in terms of the hyperbolic function and the fractional-order α. For small v compared with the speed of light c (i.e., v≪c), our results tend to Newtonian mechanics, i.e., t→t0. For v comparable to c such as v=0.9994c, our numerical results are compared with the experimental ones for the TD of the muon particles μ+. Moreover, the influence of the arbitrary-order α on the FTD is analyzed. It is also declared that at a specific α, there is an agreement between the present theoretical results and the corresponding experimental ones for the muon particles μ+. Full article
(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)
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10 pages, 263 KiB  
Article
Novel Contributions to the System of Fractional Hamiltonian Equations
by Tayeb Mahrouz, Abdelaziz Mennouni, Abdelkader Moumen and Tariq Alraqad
Mathematics 2023, 11(13), 3016; https://doi.org/10.3390/math11133016 - 7 Jul 2023
Viewed by 727
Abstract
This work aims to analyze a new system of two fractional Hamiltonian equations. We propose an effective method for transforming the established model into a system of two distinct equations. Two functionals that are connected to the converted system of fractional Hamiltonian systems [...] Read more.
This work aims to analyze a new system of two fractional Hamiltonian equations. We propose an effective method for transforming the established model into a system of two distinct equations. Two functionals that are connected to the converted system of fractional Hamiltonian systems are introduced together with a new space, and it is demonstrated that these functionals are bounded below on this space. The hypotheses presented here differ from those provided in the literature. Full article
(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)
13 pages, 2035 KiB  
Article
A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations
by Hassan Kamil Jassim and Mohammed Abdulshareef Hussein
Mathematics 2023, 11(7), 1565; https://doi.org/10.3390/math11071565 - 23 Mar 2023
Cited by 10 | Viewed by 2283
Abstract
Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields. In this paper, a new approach called the Hussein–Jassim (HJ) method is presented for solving nonlinear fractional ordinary [...] Read more.
Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields. In this paper, a new approach called the Hussein–Jassim (HJ) method is presented for solving nonlinear fractional ordinary differential equations. The new method is based on a power series of fractional order. The proposed approach is employed to obtain an approximate solution for the fractional differential equations. The results of this study show that the solutions obtained from solving the fractional differential equations are highly consistent with those obtained by exact solutions. Full article
(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)
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