Advances in Boundary Value Problems for Fractional Differential Equations, 3rd Edition

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

Deadline for manuscript submissions: 20 April 2025 | Viewed by 1341

Special Issue Editor


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Guest Editor
Department of Mathematics, "Gheorghe Asachi" Technical University of Iasi, Blvd. Carol I, nr. 11, 700506 Iasi, Romania
Interests: fractional differential equations; ordinary differential equations; partial differential equations; finite difference equations; boundary value problems
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Special Issue Information

Dear Colleagues,

Fractional differential equations have extensive applications in the mathematical modelling of real-world phenomena which occur in scientific and engineering disciplines. This Special Issue will cover new aspects of the recent developments in the theory and applications of fractional differential equations, inclusions, inequalities, and systems of fractional differential equations with Riemann-Liouville, Caputo, and Hadamard derivatives or other generalized fractional derivatives, subject to various initial and boundary conditions. Problems such as the existence, uniqueness, multiplicity, and nonexistence of solutions or positive solutions, the stability of solutions, and numerical computations for these models are of great interest for readers who work in this field.

Also, please feel free to read and download all the published articles in our first volume:

https://www.mdpi.com/journal/fractalfract/special_issues/BVP_FDE

Our second volume is also available:

https://www.mdpi.com/journal/fractalfract/special_issues/BVP_FDE2

Prof. Dr. Rodica Luca
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. 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

  • fractional differential equations
  • fractional differential inclusions
  • fractional differential inequalities
  • initial value problems
  • boundary value problems
  • existence and nonexistence
  • uniqueness and multiplicity
  • stability
  • numerical computations

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Published Papers (2 papers)

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Research

13 pages, 289 KiB  
Article
Existence, Uniqueness, and Stability of Solutions for Nabla Fractional Difference Equations
by Nikolay D. Dimitrov and Jagan Mohan Jonnalagadda
Fractal Fract. 2024, 8(10), 591; https://doi.org/10.3390/fractalfract8100591 - 8 Oct 2024
Viewed by 659
Abstract
In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some sufficient conditions in order to ensure [...] Read more.
In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some sufficient conditions in order to ensure existence and uniqueness results. Also, we establish some conditions under which the solution to the considered problem is generalized Ulam–Hyers–Rassias stable. In the end, some examples are included in order to illustrate our main results. Full article
27 pages, 406 KiB  
Article
Positive Solutions to a System of Coupled Hadamard Fractional Boundary Value Problems
by Alexandru Tudorache and Rodica Luca
Fractal Fract. 2024, 8(9), 543; https://doi.org/10.3390/fractalfract8090543 - 19 Sep 2024
Viewed by 457
Abstract
We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled nonlocal boundary conditions encompassing Riemann–Stieltjes integrals and Hadamard [...] Read more.
We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled nonlocal boundary conditions encompassing Riemann–Stieltjes integrals and Hadamard fractional derivatives. To establish the main results, we employ several fixed-point theorems, namely the Banach contraction mapping principle, the Schauder fixed-point theorem, the Leggett–Williams fixed-point theorem, and the Guo–Krasnosel’skii fixed-point theorem. Full article
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