Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel’skii fixed-point theorem we prove, via the Kolmogorov–Riesz criteria, the existence of solutions. The e...

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Published inAxioms Vol. 11; no. 6; p. 295
Main Authors Boucenna, Djalal, Chidouh, Amar, Torres, Delfim F. M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2022
Subjects
Banach spaces
Boundary conditions
Boundary value problems
Differential equations
Existence theorems
fixed point theorems
Fixed point theory
Fixed points (mathematics)
Fractional calculus
fractional differential equations
Kolmogorov–Riesz theorem
Mathematical research
Nemytskii operator
Rheology
Algeria
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Summary:We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel’skii fixed-point theorem we prove, via the Kolmogorov–Riesz criteria, the existence of solutions. The existence results are established in a specific fractional derivative Banach space and they are illustrated by two numerical examples.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11060295