Special Issue "Fractional Differential Equations, Inclusions and Inequalities with Applications II"

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

Deadline for manuscript submissions: 31 October 2022 | Viewed by 1928

Special Issue Editor

Special Issue Information

Dear Colleagues,

During the last few decades, fractional differential equations, inclusions, and inequalities have been studied extensively. As a matter of fact, fractional derivatives and integrals provide a much better tool for the description of memory and hereditary properties of various materials and processes than integer derivatives. Engineers and scientists have developed new precise models that involve fractional differential equations and inequalities. These models have been applied successfully, e.g., in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electroanalytical chemistry, control theory, etc.

The purpose of this Special Issue is to establish a collection of articles that reflect the latest mathematical developments in the field of fractional differential equations, inclusions, and inequalities with their applications.

Prof. Dr. Sotiris K. Ntouyas
Guest Editor

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Keywords

  • fractional differential equations
  • fractional differential inclusions
  • fractional inequalities
  • boundary value problem
  • existence

Published Papers (3 papers)

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Research

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Article
Sequential Fractional Hybrid Inclusions: A Theoretical Study via Dhage’s Technique and Special Contractions
Mathematics 2022, 10(12), 2090; https://doi.org/10.3390/math10122090 - 16 Jun 2022
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Abstract
The most important objective of the present research is to establish some theoretical existence results on a novel combined configuration of a Caputo sequential inclusion problem and the hybrid integro-differential one in which the boundary conditions are also formulated as the hybrid multi-order [...] Read more.
The most important objective of the present research is to establish some theoretical existence results on a novel combined configuration of a Caputo sequential inclusion problem and the hybrid integro-differential one in which the boundary conditions are also formulated as the hybrid multi-order integro-differential conditions. In this respect, firstly, some inequalities are proven in relation to the corresponding integral equation. Then, we employ some newly defined theoretical techniques with the help of the product operators on a Banach algebra and also with the aid of some special functions including α-ψ-contractions and α-admissible mappings to extract the existence criteria corresponding to the given mixed sequential hybrid BVPs. Some important useful properties such as the approximate endpoint property, (Cα)-property, and the compactness play a key role in this regard. The final part of the manuscript is devoted to formulating and computing two applicable examples to guarantee the correctness of the obtained results. Full article
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Article
Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions
Mathematics 2022, 10(5), 767; https://doi.org/10.3390/math10050767 - 28 Feb 2022
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Abstract
In this paper, we study the existence of solutions to a fractional (p, q)-difference equation equipped with separate local boundary value conditions. The uniqueness of solutions is established by means of Banach’s contraction mapping principle, while the existence [...] Read more.
In this paper, we study the existence of solutions to a fractional (p, q)-difference equation equipped with separate local boundary value conditions. The uniqueness of solutions is established by means of Banach’s contraction mapping principle, while the existence results of solutions are obtained by applying Krasnoselskii’s fixed-point theorem and the Leary–Schauder alternative. Some examples illustrating the main results are also presented. Full article

Review

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Review
A Survey on the Oscillation of Solutions for Fractional Difference Equations
Mathematics 2022, 10(6), 894; https://doi.org/10.3390/math10060894 - 11 Mar 2022
Cited by 1 | Viewed by 619
Abstract
In this paper, we present a systematic study concerning the developments of the oscillation results for the fractional difference equations. Essential preliminaries on discrete fractional calculus are stated prior to giving the main results. Oscillation results are presented in a subsequent order and [...] Read more.
In this paper, we present a systematic study concerning the developments of the oscillation results for the fractional difference equations. Essential preliminaries on discrete fractional calculus are stated prior to giving the main results. Oscillation results are presented in a subsequent order and for different types of equations. The investigation was carried out within the delta and nabla operators. Full article
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