Positive Solutions to a System of Coupled Hadamard Fractional Boundary Value Problems

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–Sti...

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Bibliographic Details
Published inFractal and fractional Vol. 8; no. 9; p. 543
Main Authors Tudorache, Alexandru, Luca, Rodica
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2024
Subjects
Boundary conditions
Boundary value problems
Differential equations
existence
Fixed points (mathematics)
Fractional calculus
Hadamard fractional differential equations
Integrals
Laws, regulations and rules
multiplicity
nonlocal coupled boundary conditions
positive solutions
Rocks, Igneous
Schauder fixpoint theorem
uniqueness
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Summary: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.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8090543