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Symmetry
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Applied Mathematics and Fractional Calculus III
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Applied Mathematics and Fractional Calculus III

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 2887

Special Issue Editors

Dr. Mohammed K. A. Kaabar

E-Mail Website
Guest Editor
Chinese Institute of Electric Power, Samarkand International University of Technology, Samarkand 140100, Uzbekistan
Interests: mathematics; electrical engineering; computer engineering; antennas and wave propagation; modern electronics; data analysis; design project; sustainable development; new technology
Special Issues, Collections and Topics in MDPI journals
Dr. Francisco Martínez González

E-Mail Website
Guest Editor
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, Spain
Interests: fractional calculus; real analysis; complex analysis; mathematical physics; numerical analysis; computational science; mathematical modeling; theoretical physics; signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the great success of our Special Issue "Applied Mathematics and Fractional Calculus & II" we decided to set up the third volume.

In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. That is why the application of fractional calculus theory has become a focus of international academic research.

Welcome to read the publications in "Applied Mathematics and Fractional Calculus & II" at https://www.mdpi.com/journal/symmetry/special_issues/Applied_Mathematics_Fractional_Calculus and https://www.mdpi.com/journal/symmetry/special_issues/Applied_Mathematics_Fractional_Calculus_II.

Dr. Mohammed K. A. Kaabar
Dr. Francisco Martínez González
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. Symmetry 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
  • fractional derivative
  • fractional integral
  • multivariable fractional calculus
  • fractional differential equations
  • fractional partial derivative equations
  • fractional physical equations

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Related Special Issue

Published Papers (2 papers)

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Research

30 pages, 3131 KiB  
Article
A New Fractional Curvature of Curves and Surfaces in Euclidean Space Using the Caputo’s Fractional Derivative
by Franco Rubio-López, Obidio Rubio, Ronald León, Alexis Rodriguez and Daniel Chucchucan
Symmetry 2024, 16(10), 1350; https://doi.org/10.3390/sym16101350 - 11 Oct 2024
Viewed by 1162
Abstract
In this paper, the authors generalize the fractional curvature of plane curves introduced by Rubio et al. in 2023, to regular curves in the Euclidean space R3, and study the geometric properties of the curve using Caputo’s fractional derivative. Furthermore, we [...] Read more.
In this paper, the authors generalize the fractional curvature of plane curves introduced by Rubio et al. in 2023, to regular curves in the Euclidean space R3, and study the geometric properties of the curve using Caputo’s fractional derivative. Furthermore, we introduce a new definition of fractional curvature and fractional mean curvature of a regular surface, using fractional principal curvatures; and prove that such concepts are invariant under isometries; i.e., they belong to the intrinsic geometry of the regular surface. Also, a geometric interpretation is given to Caputo’s fractional derivative of algebraic polynomials. Full article
(This article belongs to the Special Issue Applied Mathematics and Fractional Calculus III)
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14 pages, 509 KiB  
Article
The Existence and Averaging Principle for a Class of Fractional Hadamard Itô–Doob Stochastic Integral Equations
by Mohamed Rhaima, Lassaad Mchiri and Abdellatif Ben Makhlouf
Symmetry 2023, 15(10), 1910; https://doi.org/10.3390/sym15101910 - 12 Oct 2023
Cited by 2 | Viewed by 1033
Abstract
In this paper, we investigate the existence and uniqueness properties pertaining to a class of fractional Hadamard Itô–Doob stochastic integral equations (FHIDSIE). Our study centers around the utilization of the Picard iteration technique (PIT), which not only establishes these fundamental properties but also [...] Read more.
In this paper, we investigate the existence and uniqueness properties pertaining to a class of fractional Hadamard Itô–Doob stochastic integral equations (FHIDSIE). Our study centers around the utilization of the Picard iteration technique (PIT), which not only establishes these fundamental properties but also unveils the remarkable averaging principle within FHIDSIE. To accomplish this, we harness powerful mathematical tools, including the Hölder and Gronwall inequalities. Full article
(This article belongs to the Special Issue Applied Mathematics and Fractional Calculus III)
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