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Mathematics
Special Issues
Recent Research on Fractional Calculus: Theory and Applications
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Special Issue "Recent Research on Fractional Calculus: Theory and Applications"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 31 March 2024 | Viewed by 988

Special Issue Editors

Dr. Faïçal Ndaïrou

E-Mail Website
Guest Editor
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
Interests: fractional calculus; mathematical biology; optimal control
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

Special Issue Information

Dear Colleagues,

Fractional calculus is a theory that unifies differential and integral operators of arbitrary (integer and non-integer) orders to form differintegral operators. The theory is becoming more attractive due to its applicability to real-world problems, such as describing biological phenomena that are memory-dependent. The aim of this Special Issue is to contribute advancements in fractional calculus, both from theoretical and applicational points of view. We welcome papers on the following topics:

  • Properties of fractional operators defined by new kernels functions;
  • Static and dynamic optimization methods based on fractional operators;
  • Fractional nonlinear dynamical systems and control;
  • Mathematics of infectious diseases by fractional operators.

Dr. Faïçal Ndaïrou
Prof. Dr. Delfim F. M. Torres
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.

Keywords

  • fractional operators
  • differintegral operators
  • memory-dependent phenomena
  • optimal control
  • mathematical modeling
  • bio-mathematics

Published Papers (2 papers)

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Article
New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses
by
Abdellatif Benchaib
,
Abdelkrim Salim
,
Saïd Abbas
and
Mouffak Benchohra
Mathematics 2023, 11(16), 3490; https://doi.org/10.3390/math11163490 - 12 Aug 2023
Viewed by 347
Abstract
This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces. Our objective is to establish adequate conditions that ensure the existence, uniqueness, and Ulam–Hyers–Rassias stability results for our problems. The studied [...] Read more.
This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces. Our objective is to establish adequate conditions that ensure the existence, uniqueness, and Ulam–Hyers–Rassias stability results for our problems. The studied problems encompass abstract impulsive fractional differential problems with finite delay, infinite delay, state-dependent finite delay, and state-dependent infinite delay. To provide clarity and depth, we augment our theoretical results with illustrative examples, illustrating the practical implications of our work. Full article
(This article belongs to the Special Issue Recent Research on Fractional Calculus: Theory and Applications)
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Article
Euler–Lagrange-Type Equations for Functionals Involving Fractional Operators and Antiderivatives
by
Ricardo Almeida
Mathematics 2023, 11(14), 3208; https://doi.org/10.3390/math11143208 - 21 Jul 2023
Viewed by 271
Abstract
The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set C1[a,b], must satisfy. The Lagrange function depends on a generalized [...] Read more.
The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set C1[a,b], must satisfy. The Lagrange function depends on a generalized fractional derivative, on a generalized fractional integral, and on an antiderivative involving the previous fractional operators. We begin by obtaining the fractional Euler–Lagrange equation, which is a necessary condition to optimize a given functional. By imposing convexity conditions over the Lagrange function, we prove that it is also a sufficient condition for optimization. After this, we consider variational problems with additional constraints on the set of admissible functions, such as the isoperimetric and the holonomic problems. We end by considering a generalization of the fundamental problem, where the fractional order is not restricted to real values between 0 and 1, but may take any positive real value. We also present some examples to illustrate our results. Full article
(This article belongs to the Special Issue Recent Research on Fractional Calculus: Theory and Applications)
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