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Axioms
Special Issues
Fractional Calculus and Differential Equations
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Fractional Calculus and Differential Equations

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 6569

Special Issue Editors

Prof. Dr. Guotao Wang

E-Mail Website
Guest Editor
School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China
Interests: fractional calculus and applications; differential equations & nonlinear analysis; integral equation and inequalities; fractional Laplacian problem; Hessian equation; Monge–Ampere equation; modern analytical methods and their applications
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Delfim F. M. Torres

grade E-Mail Website
Guest Editor
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Interests: fractional calculus; dynamics on time scales; mathematical biology; calculus of variations; optimal control
Special Issues, Collections and Topics in MDPI journals
Dr. Abdelhamid Djaouti

E-Mail Website
Guest Editor
Department of the Preparatory Year, King Faisal University, Al Hofuf 36362, Saudi Arabia
Interests: linear partial differential equations and their applications; non-linear partial differential equations and their applications; fractional calculus

Special Issue Information

Dear Colleagues,

Differential equations (ordinary differential equations, partial differential equations, stochastic differential equations, etc.) are indispensable in modeling various phenomena and processes in physics, chemical reactions, engineering, biological processes and social sciences. The main goal of this Special Issue is to channel activities and resources to develop and promote different research topics in the analysis of differential equations and its applications. Moreover, in this Special Issue we hope to interact with other topics like fractional operators and their applications in linear or nonlinear differential equations, generalized functions, and applications of harmonic analysis.

Before submission, authors should carefully read over the journal's Instructions for Authors at https://0-www-mdpi-com.brum.beds.ac.uk/journal/axioms/instructions. We are hopeful that the manuscripts submitted will have a high mathematical level. Topics that are invited for submission include (but are not limited to):

  • Linear and nonlinear differential equations;
  • Fractional calculus and applications;
  • Ordinary differential equations;
  • Partial differential equations;
  • Stochastic differential equations;
  • Fuzzy differential equations;
  • Harmonic analysis and applications;
  • Applications to real-world phenomena;
  • Related topics about differential equations.

Prof. Dr. Guotao Wang
Prof. Dr. Delfim F. M. Torres
Dr. Abdelhamid Mohammed Djaouti
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. Axioms 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

  • linear and nonlinear differential equations
  • fractional calculus and applications
  • ordinary differential equations
  • partial differential equations
  • stochastic differential equations
  • fuzzy differential equations
  • harmonic analysis and applications

Published Papers (4 papers)

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Research

20 pages, 353 KiB  
Article
Fractional Nonlinearity for the Wave Equation with Friction and Viscoelastic Damping
by Abdelhamid Mohammed Djaouti and Muhammad Amer Latif
Axioms 2022, 11(10), 524; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11100524 - 01 Oct 2022
Viewed by 1166
Abstract
In this paper we consider a fractional nonlinearity for the wave equation with friction and viscoelastic damping. Using Fixed point theorem a global in time existence of small data solutions to the Cauchy problem is investigated in this research. Our main interest is [...] Read more.
In this paper we consider a fractional nonlinearity for the wave equation with friction and viscoelastic damping. Using Fixed point theorem a global in time existence of small data solutions to the Cauchy problem is investigated in this research. Our main interest is to show the influence of the fractional nonlinearity parameter to the admissible range of exponent ς comparing with power nonlinearity and also the generating of loss of decay. Full article
(This article belongs to the Special Issue Fractional Calculus and Differential Equations)
11 pages, 500 KiB  
Article
On Implicit Time–Fractal–Fractional Differential Equation
by McSylvester Ejighikeme Omaba, Soh Edwin Mukiawa and Eze R. Nwaeze
Axioms 2022, 11(7), 348; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11070348 - 20 Jul 2022
Viewed by 1170
Abstract
An implicit time–fractal–fractional differential equation involving the Atangana’s fractal–fractional derivative in the sense of Caputo with the Mittag–Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an [...] Read more.
An implicit time–fractal–fractional differential equation involving the Atangana’s fractal–fractional derivative in the sense of Caputo with the Mittag–Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an exponential growth bound, and, consequently, the long-time (asymptotic) property of the solution. We also give examples to illustrate our problem. Full article
(This article belongs to the Special Issue Fractional Calculus and Differential Equations)
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16 pages, 296 KiB  
Article
The Existence of Radial Solutions to the Schrödinger System Containing a Nonlinear Operator
by Guotao Wang, Zhuobin Zhang and Zedong Yang
Axioms 2022, 11(6), 282; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11060282 - 10 Jun 2022
Cited by 1 | Viewed by 1261
Abstract
In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ [...] Read more.
In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ and ν are bounded, μ and ν are blow-up, and one of the components is bounded, while the other is blow-up. Finally, we present two examples to verify our results. Full article
(This article belongs to the Special Issue Fractional Calculus and Differential Equations)
10 pages, 283 KiB  
Article
Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels
by Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres and Noura Yousfi
Axioms 2022, 11(5), 231; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11050231 - 15 May 2022
Cited by 7 | Viewed by 2036
Abstract
We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators [...] Read more.
We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor’s and mean value theorems for Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) and weighted ABC derivatives. Full article
(This article belongs to the Special Issue Fractional Calculus and Differential Equations)
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