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Fractal Fract
Special Issues
Abstract Fractional Differential Inclusions
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Abstract Fractional Differential Inclusions

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 4025

Special Issue Editors

Prof. Dr. Marko Kostić

E-Mail Website
Guest Editor
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad 21125, Serbia
Interests: functional analysis and partial differential equations
Prof. Dr. Wei-Shih Du

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus and fractional differential equations are rapidly growing research fields, primarily from their incredible importance in modelling the various phenomena appearing in pure and applied science. It would be difficult to summarize here all relevant applications of fractional calculus and fractional differential equations in engineering, physics, chemistry, aerodynamics, economics, and other sciences.

The theory of abstract fractional differential inclusions can be viewed as an important part of the theory of abstract Volterra integro-differential inclusions, which is still a very active field of investigation.

This Special Issue aims to present recent developments in the theory of abstract fractional integro-differential inclusions in adequate detail. Topics invited for submission include (but are not limited to):

  • Fractional calculus and scalar-valued fractional differential equations;
  • Abstract Volterra integro-differential equations and inclusions;
  • Abstract fractional integro-differential equations and inclusions;
  • Almost periodic type solutions of abstract Volterra integro-differential equations and inclusions;
  • Stability, positivity, and exponential decaying of fractional solution operator families;
  • Linear topological dynamics of abstract fractional integro-differential equations and inclusions;
  • Applications of fractional integro-differential equations and inclusions.

Prof. Dr. Marko Kostić
Prof. Dr. Wei-Shih Du
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. Fractal and Fractional 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 2700 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

  • abstract volterra integro-differential inclusions
  • abstract fractional integro-differential inclusions
  • scalar fractional integro-differential inclusions
  • almost periodic type solutions of abstract fractional integro-differential inclusions
  • chaotic solutions of abstract fractional integro-differential inclusions
  • fractional calculus

Published Papers (4 papers)

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Research

17 pages, 351 KiB  
Article
Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family
by Jia Mu, Zhiyuan Yuan and Yong Zhou
Fractal Fract. 2023, 7(11), 785; https://doi.org/10.3390/fractalfract7110785 - 27 Oct 2023
Viewed by 968
Abstract
Fractional integrodifferential diffusion equations play a significant role in describing anomalous diffusion phenomena. In this paper, we study the existence and uniqueness of mild solutions to these equations. Firstly, we construct an appropriate resolvent family, through which the related equicontinuity, strong continuity, and [...] Read more.
Fractional integrodifferential diffusion equations play a significant role in describing anomalous diffusion phenomena. In this paper, we study the existence and uniqueness of mild solutions to these equations. Firstly, we construct an appropriate resolvent family, through which the related equicontinuity, strong continuity, and compactness properties are studied using the convolution theorem of Laplace transform, the probability density function, the Cauchy integral formula, and the Fubini theorem. Then, we construct a reasonable mild solution for the considered equations. Finally, we obtain some sufficient conditions for the existence and uniqueness of mild solutions to the considered equations by some fixed point theorems. Full article
(This article belongs to the Special Issue Abstract Fractional Differential Inclusions)
24 pages, 468 KiB  
Article
Generalized ρ-Almost Periodic Sequences and Applications
by Marko Kostić, Belkacem Chaouchi, Wei-Shih Du and Daniel Velinov
Fractal Fract. 2023, 7(5), 410; https://doi.org/10.3390/fractalfract7050410 - 18 May 2023
Cited by 1 | Viewed by 791
Abstract
In this paper, we analyze the Bohr ρ-almost periodic type sequences and the generalized ρ-almost periodic type sequences of the form F:I×X→Y, where ∅≠I⊆Zn, X and Y are [...] Read more.
In this paper, we analyze the Bohr ρ-almost periodic type sequences and the generalized ρ-almost periodic type sequences of the form F:I×X→Y, where ∅≠I⊆Zn, X and Y are complex Banach spaces and ρ is a general binary relation on Y. We provide many structural results, observations and open problems about the introduced classes of ρ-almost periodic sequences. Certain applications of the established theoretical results to the abstract Volterra integro-difference equations are also given. Full article
(This article belongs to the Special Issue Abstract Fractional Differential Inclusions)
15 pages, 338 KiB  
Article
Quasilinear Fractional Order Equations and Fractional Powers of Sectorial Operators
by Vladimir E. Fedorov, Marko Kostić and Tatyana A. Zakharova
Fractal Fract. 2023, 7(5), 385; https://doi.org/10.3390/fractalfract7050385 - 05 May 2023
Viewed by 878
Abstract
The fractional powers of generators for analytic operator semigroups are used for the proof of the existence and uniqueness of a solution of the Cauchy problem to a first order semilinear equation in a Banach space. Here, we use an analogous construction of [...] Read more.
The fractional powers of generators for analytic operator semigroups are used for the proof of the existence and uniqueness of a solution of the Cauchy problem to a first order semilinear equation in a Banach space. Here, we use an analogous construction of fractional powers Aγ for an operator A such that −A generates analytic resolving families of operators for a fractional order equation. Under the condition of local Lipschitz continuity with respect to the graph norm of Aγ for some γ∈(0,1) of a nonlinear operator, we prove the local unique solvability of the Cauchy problem to a fractional order quasilinear equation in a Banach space with several Gerasimov–Caputo fractional derivatives in the nonlinear part. An analogous nonlocal Lipschitz condition is used to obtain a theorem of the nonlocal unique solvability of the Cauchy problem. Abstract results are applied to study an initial-boundary value problem for a time-fractional order nonlinear diffusion equation. Full article
(This article belongs to the Special Issue Abstract Fractional Differential Inclusions)
15 pages, 343 KiB  
Article
Weak Solution for a Fractional Langevin Inclusion with the Katugampola–Caputo Fractional Derivative
by Lamya Almaghamsi
Fractal Fract. 2023, 7(2), 174; https://doi.org/10.3390/fractalfract7020174 - 09 Feb 2023
Viewed by 817
Abstract
In this work, we examine the existence of weak solution for a class of boundary value problems involving fractional Langevin inclusion with the Katugampola–Caputo fractional derivative under specified conditions contain the Pettis integrability assumption. The Mönch fixed point theorem is used with the [...] Read more.
In this work, we examine the existence of weak solution for a class of boundary value problems involving fractional Langevin inclusion with the Katugampola–Caputo fractional derivative under specified conditions contain the Pettis integrability assumption. The Mönch fixed point theorem is used with the weak noncompactness measure approach to investigate the existence results. In order to illustrate our results, we present an example. Full article
(This article belongs to the Special Issue Abstract Fractional Differential Inclusions)
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