Recent Investigations of Differential and Fractional Equations and Inclusions, 3rd Edition

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 2025 | Viewed by 2029

Special Issue Editor


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Department of Applied Mathematics and Modeling, University of Plovdiv, Paisii Hilendarski, 4002 Plovdiv, Bulgaria
Interests: differential equations; delays; impulses; difference equations; fractional differential equations
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Special Issue Information

Dear Colleagues,

During the past decades, the subject of the calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and importance. This is mainly due to its demonstrated applications in numerous, seemingly diverse and widespread fields of science and engineering.

This Special Issue invites papers that focus on recent and novel developments in the theory of any types of differential and fractional differential equations and inclusions, especially on analytical and numerical results for fractional ordinary and partial differential equations.

This Special Issue will accept high-quality papers containing original research results and survey articles of exceptional merit in the following fields:

  • Differential equations and inclusions;
  • Differential equations and inclusions with impulses;
  • Delay differential equations;
  • Fuzzy differential and integral equations;
  • Fractional differential equations and inclusions;
  • Difference equations;
  • Discrete fractional equations;
  • Dynamical models with differential, fractional, difference, or fuzzy equations.

Prof. Dr. Snezhana Hristova
Guest Editor

Manuscript Submission Information

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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

  • differential equations
  • differential inclusions
  • fuzzy differential and integral equations
  • fractional differential equations
  • difference equations
  • dynamical models

Related Special Issue

Published Papers (3 papers)

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Research

12 pages, 287 KiB  
Article
Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System
by Mouataz Billah Mesmouli, Loredana Florentina Iambor, Amir Abdel Menaem and Taher S. Hassan
Mathematics 2024, 12(9), 1399; https://doi.org/10.3390/math12091399 - 3 May 2024
Viewed by 391
Abstract
In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional p,q-difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a [...] Read more.
In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional p,q-difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a unique solution. By Krasnoselskii’s fixed-point theorem, we prove the existence of solutions. In addition, finite stability has been established too. The main results in the literature have been proven to be a particular corollary of our work. Full article
21 pages, 326 KiB  
Article
Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function
by Sotiris K. Ntouyas, Phollakrit Wongsantisuk, Ayub Samadi and Jessada Tariboon
Mathematics 2024, 12(7), 1071; https://doi.org/10.3390/math12071071 - 2 Apr 2024
Viewed by 522
Abstract
In this paper, a new class of coupled hybrid systems of proportional sequential ψ-Hilfer fractional differential equations, subjected to nonlocal boundary conditions were investigated. Based on a generalization of the Krasnosel’skii˘’s fixed point theorem due to Burton, sufficient conditions [...] Read more.
In this paper, a new class of coupled hybrid systems of proportional sequential ψ-Hilfer fractional differential equations, subjected to nonlocal boundary conditions were investigated. Based on a generalization of the Krasnosel’skii˘’s fixed point theorem due to Burton, sufficient conditions were established for the existence of solutions. A numerical example was constructed illustrating the main theoretical result. For special cases of the parameters involved in the system many new results were covered. The obtained result is new and significantly contributes to existing results in the literature on coupled systems of proportional sequential ψ-Hilfer fractional differential equations. Full article
16 pages, 327 KiB  
Article
Existence and Stability Results for Differential Equations with a Variable-Order Generalized Proportional Caputo Fractional Derivative
by Donal O’Regan, Ravi P. Agarwal, Snezhana Hristova and Mohamed I. Abbas
Mathematics 2024, 12(2), 233; https://doi.org/10.3390/math12020233 - 11 Jan 2024
Cited by 1 | Viewed by 824
Abstract
An initial value problem for a scalar nonlinear differential equation with a variable order for the generalized proportional Caputo fractional derivative is studied. We consider the case of a piecewise constant variable order of the fractional derivative. Since the order of the fractional [...] Read more.
An initial value problem for a scalar nonlinear differential equation with a variable order for the generalized proportional Caputo fractional derivative is studied. We consider the case of a piecewise constant variable order of the fractional derivative. Since the order of the fractional integrals and derivatives depends on time, we will consider several different cases. The argument of the variable order could be equal to the current time or it could be equal to the variable of the integral determining the fractional derivative. We provide three different definitions of generalized proportional fractional integrals and Caputo-type derivatives, and the properties of the defined differentials/integrals are discussed and compared with what is known in the literature. Appropriate auxiliary systems with constant-order fractional derivatives are defined and used to construct solutions of the studied problem in the three cases of fractional derivatives. Existence and uniqueness are studied. Also, the Ulam-type stability is defined in the three cases, and sufficient conditions are obtained. The suggested approach is more broadly based, and the same methodology can be used in a number of additional issues. Full article
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