Caputo-Hadamard fractional differential equations with nonlocal fractional integro-differential boundary conditions via topological degree theory

Choukri Derbazi; Hadda Hammouche; Choukri Derbazi; Hadda Hammouche

doi:10.3934/math.2020174

AIMS Mathematics

2020, Volume 5, Issue 3: 2694-2709. doi: 10.3934/math.2020174

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Caputo-Hadamard fractional differential equations with nonlocal fractional integro-differential boundary conditions via topological degree theory

Choukri Derbazi ^,,
Hadda Hammouche

Laboratory of Mathematics and Applied Sciences University of Ghardaia, 47000, Algeria

Received: 01 November 2019 Accepted: 12 March 2020 Published: 17 March 2020
MSC : 26A33, 34A08

This article aims to prove the existence and uniqueness of solutions to a nonlinear boundary value problem of fractional differential equations involving the Caputo-Hadamard fractional derivative with nonlocal fractional integro-differential boundary conditions. The concerned results are obtained employing topological degree for condensing maps via a priori estimate method and the Banach contraction principle fixed point theorem. Besides, two illustrative examples are presented.
- fractional differential equations,
- Caputo-Hadamard derivative,
- fractional integral conditions,
- existence,
- uniqueness,
- topological degree theory,
- condensing maps
Citation: Choukri Derbazi, Hadda Hammouche. Caputo-Hadamard fractional differential equations with nonlocal fractional integro-differential boundary conditions via topological degree theory[J]. AIMS Mathematics, 2020, 5(3): 2694-2709. doi: 10.3934/math.2020174

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Abstract

This article aims to prove the existence and uniqueness of solutions to a nonlinear boundary value problem of fractional differential equations involving the Caputo-Hadamard fractional derivative with nonlocal fractional integro-differential boundary conditions. The concerned results are obtained employing topological degree for condensing maps via a priori estimate method and the Banach contraction principle fixed point theorem. Besides, two illustrative examples are presented.

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