Special Issue "Initial and Boundary Value Problems for Differential Equations"

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

Deadline for manuscript submissions: 15 December 2022 | Viewed by 3165

Special Issue Editors

Dr. Bashir Ahmad
E-Mail Website
Guest Editor
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
Interests: differential equations; stability; mathematical analysis; fixed point theory; fractional differential equations
Dr. Jessada Tariboon
E-Mail Website
Guest Editor
Department of Mathematics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
Interests: differential equations; boundary value problems; nonlinear analysis applications

Special Issue Information

Dear Colleagues,

The importance of initial and boundary value problems of different kinds of differential equations (ordinary, functional, fractional, partial, difference, stochastic, integral, etc.) is well recognized in view of their extensive applications in applied sciences and engineering.

Single-valued and multi-valued initial and boundary value problems involving different kinds of boundary conditions have attracted significant attention during the last few decades. The literature on this topic is now much enriched and contains a variety of results ranging from the existence theory to the methods of solution for such problems. The techniques of functional analysis and fixed-point theory play a key role in proving the existence and uniqueness of solutions to these problems.

The aim of this Special Issue is to strengthen the available literature on the topic by publishing research and review articles on initial and boundary value problems of differential equations and inclusions in a broader sense.

Potential topics include but are not limited to:

Existence, uniqueness, and multiplicity results for initial and boundary value problems for differential equations and inclusions (ordinary, functional, fractional, partial, difference, stochastic, integral, etc.)

Prof. Dr. Sotiris K. Ntouyas
Dr. Jessada Tariboon
Dr. Bashir Ahmad
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 1800 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

  • qualitative properties of the solutions (positivity, oscillation, asymptotic behavior, stability, etc.)
  • topological methods in differential equations and inclusions
  • approximation of the solutions
  • eigenvalue problems
  • variational methods
  • fixed point theory
  • critical point theory
  • applications to real-world phenomena

Published Papers (7 papers)

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Research

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Article
Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order
Fractal Fract. 2022, 6(7), 358; https://doi.org/10.3390/fractalfract6070358 - 26 Jun 2022
Viewed by 209
Abstract
We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space Rm. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability [...] Read more.
We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space Rm. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability of the solutions. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
Article
Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers
Fractal Fract. 2022, 6(7), 352; https://doi.org/10.3390/fractalfract6070352 - 23 Jun 2022
Viewed by 226
Abstract
By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: [...] Read more.
By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: (Δ)α2u(x)+uγ(x)+vq(x)=0,xRN, (Δ)β2v(x)+vσ(x)+up(x)=0,xRN, u(x)|x|a,v(x)|x|bas|x|, where α,β(0,2), and a,b>0 are constants. We study the decay at infinity and narrow region principle for the fractional Laplacian system with different negative powers. The same results hold for nonlinear Hénon-type fractional Laplacian systems with different negative powers. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
Article
Existence and Stability Results for a Tripled System of the Caputo Type with Multi-Point and Integral Boundary Conditions
Fractal Fract. 2022, 6(6), 285; https://doi.org/10.3390/fractalfract6060285 - 26 May 2022
Viewed by 419
Abstract
In this paper, we introduce and investigate the existence and stability of a tripled system of sequential fractional differential equations (SFDEs) with multi-point and integral boundary conditions. The existence and uniqueness of the solutions are established by the principle of Banach’s contraction and [...] Read more.
In this paper, we introduce and investigate the existence and stability of a tripled system of sequential fractional differential equations (SFDEs) with multi-point and integral boundary conditions. The existence and uniqueness of the solutions are established by the principle of Banach’s contraction and the alternative of Leray–Schauder. The stability of the Hyer–Ulam solutions are investigated. A few examples are provided to identify the major results. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
Article
Nonlocal Coupled System for (k,φ)-Hilfer Fractional Differential Equations
Fractal Fract. 2022, 6(5), 234; https://doi.org/10.3390/fractalfract6050234 - 23 Apr 2022
Viewed by 552
Abstract
In this paper, we study a coupled system consisting of (k,φ)-Hilfer fractional differential equations of the order (1,2], supplemented with nonlocal coupled multi-point boundary conditions. The existence and uniqueness of the results are [...] Read more.
In this paper, we study a coupled system consisting of (k,φ)-Hilfer fractional differential equations of the order (1,2], supplemented with nonlocal coupled multi-point boundary conditions. The existence and uniqueness of the results are established via Banach’s contraction mapping principle, the Leray–Schauder alternative and Krasnosel’skiĭ’s fixed-point theorem. Numerical examples are constructed to illustrate the obtained results. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
Article
Some Fixed-Disc Results in Double Controlled Quasi-Metric Type Spaces
Fractal Fract. 2022, 6(2), 107; https://doi.org/10.3390/fractalfract6020107 - 12 Feb 2022
Viewed by 403
Abstract
In this paper, we introduce new types of general contractions for self mapping on double controlled quasi-metric type spaces, where we prove the existence and uniqueness of fixed disc and circle for such mappings. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
Article
Common Fixed Point Theorems for Two Mappings in Complete b-Metric Spaces
Fractal Fract. 2022, 6(2), 103; https://doi.org/10.3390/fractalfract6020103 - 11 Feb 2022
Viewed by 316
Abstract
Our paper is devoted to the issue of the existence and uniqueness of common fixed points for two mappings in complete b-metric spaces by virtue of the new functions F and θ, respectively. Moreover, two specific examples to indicate the validity [...] Read more.
Our paper is devoted to the issue of the existence and uniqueness of common fixed points for two mappings in complete b-metric spaces by virtue of the new functions F and θ, respectively. Moreover, two specific examples to indicate the validity of our results are also given. Eventually, the generalized forms of Jungck fixed point theorem in the above spaces is investigated. Different from related literature, the conditions that the function F needs to satisfy are weakened, and F only needs to be non-decreasing in this paper. To some extent, our conclusions and methods improve the results of previous literature. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)

Review

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Review
A Survey on Recent Results on Lyapunov-Type Inequalities for Fractional Differential Equations
Fractal Fract. 2022, 6(5), 273; https://doi.org/10.3390/fractalfract6050273 - 18 May 2022
Viewed by 448
Abstract
This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions. Our work deals with Caputo, Riemann-Liouville, ψ-Caputo, ψ-Hilfer, hybrid, Caputo-Fabrizio, Hadamard, [...] Read more.
This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions. Our work deals with Caputo, Riemann-Liouville, ψ-Caputo, ψ-Hilfer, hybrid, Caputo-Fabrizio, Hadamard, Katugampola, Hilfer-Katugampola, p-Laplacian, and proportional fractional derivative operators. Full article
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
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