Special Issue "Fractional Calculus - Theory and Applications"

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

Deadline for manuscript submissions: 31 August 2021.

Special Issue Editor

Prof. Dr. Jorge E. Macías Díaz
E-Mail Website
Guest Editor
1. Department of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia
2. Department of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes 20131, Mexico
Interests: fractional calculus; difference equations; differential equations

Special Issue Information

Dear Colleagues,

In recent years, fractional calculus has witnessed tremendous progress in various areas of sciences and mathematics. On one hand, new definitions of fractional derivatives and integrals have appeared in recent years, extending the classical definitions in some sense or another. Moreover, the rigorous analysis of the functional properties of those new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated rigorously from the analytical and numerical points of view, and potential applications have been proposed in the sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progresses in the theory of fractional calculus and its potential applications. We invite authors to submit high-quality reports on the analysis of fractional-order differential/integral equations, the analysis of new definitions of fractional derivatives, numerical methods for fractional-order equations, and applications to physical systems governed by fractional differential equations, among other interesting topics of research.

Prof. Dr. Jorge E. Macías-Díaz
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.

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Keywords

  • Fractional-order differential/integral equations
  • Existence and regularity of solutions
  • Numerical methods for fractional equations
  • Analysis of convergence and stability
  • Applications to science and technology

Published Papers (3 papers)

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Research

Article
Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions
Axioms 2021, 10(3), 130; https://doi.org/10.3390/axioms10030130 - 23 Jun 2021
Viewed by 221
Abstract
In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence [...] Read more.
In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed. Full article
(This article belongs to the Special Issue Fractional Calculus - Theory and Applications)
Article
A Comparison of a Priori Estimates of the Solutions of a Linear Fractional System with Distributed Delays and Application to the Stability Analysis
Axioms 2021, 10(2), 75; https://doi.org/10.3390/axioms10020075 - 27 Apr 2021
Viewed by 317
Abstract
In this article, we consider a retarded linear fractional differential system with distributed delays and Caputo type derivatives of incommensurate orders. For this system, several a priori estimates for the solutions, applying the two traditional approaches—by the use of the Gronwall’s inequality and [...] Read more.
In this article, we consider a retarded linear fractional differential system with distributed delays and Caputo type derivatives of incommensurate orders. For this system, several a priori estimates for the solutions, applying the two traditional approaches—by the use of the Gronwall’s inequality and by the use of integral representations of the solutions are obtained. As application of the obtained estimates, different sufficient conditions which guaranty finite-time stability of the solutions are established. A comparison of the obtained different conditions in respect to the used estimates and norms is made. Full article
(This article belongs to the Special Issue Fractional Calculus - Theory and Applications)
Article
Fractional Coupled Hybrid Sturm–Liouville Differential Equation with Multi-Point Boundary Coupled Hybrid Condition
Axioms 2021, 10(2), 65; https://doi.org/10.3390/axioms10020065 - 16 Apr 2021
Viewed by 364
Abstract
The Sturm–Liouville differential equation is an important tool for physics, applied mathematics, and other fields of engineering and science and has wide applications in quantum mechanics, classical mechanics, and wave phenomena. In this paper, we investigate the coupled hybrid version of the Sturm–Liouville [...] Read more.
The Sturm–Liouville differential equation is an important tool for physics, applied mathematics, and other fields of engineering and science and has wide applications in quantum mechanics, classical mechanics, and wave phenomena. In this paper, we investigate the coupled hybrid version of the Sturm–Liouville differential equation. Indeed, we study the existence of solutions for the coupled hybrid Sturm–Liouville differential equation with multi-point boundary coupled hybrid condition. Furthermore, we study the existence of solutions for the coupled hybrid Sturm–Liouville differential equation with an integral boundary coupled hybrid condition. We give an application and some examples to illustrate our results. Full article
(This article belongs to the Special Issue Fractional Calculus - Theory and Applications)
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