Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces

Abdelatif Boutiara; Kaddour Guerbati; Maamar Benbachir; Abdelatif Boutiara; Kaddour Guerbati; Maamar Benbachir

doi:10.3934/math.2020017

AIMS Mathematics

2020, Volume 5, Issue 1: 259-272. doi: 10.3934/math.2020017

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Research article

Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces

1.
Laboratory of Mathematics and Applied Sciences University of Ghardaia, 47000, Algeria
2.
Faculty of Sciences and Technology, Saad Dahlab University, Blida, Algeria

Received: 11 August 2019 Accepted: 23 October 2019 Published: 07 November 2019
MSC : 26A33, 34A60

We introduce a more general class of fractional-order boundary value problems involving the Caputo-Hadamard fractional derivative. Existence results for the given problem are established by applying the Mönchos fixed point theorem and the technique of measures of noncompactness. an example is given to illustrate our results. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions.
Citation: Abdelatif Boutiara, Kaddour Guerbati, Maamar Benbachir. Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces[J]. AIMS Mathematics, 2020, 5(1): 259-272. doi: 10.3934/math.2020017

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Abstract

We introduce a more general class of fractional-order boundary value problems involving the Caputo-Hadamard fractional derivative. Existence results for the given problem are established by applying the Mönchos fixed point theorem and the technique of measures of noncompactness. an example is given to illustrate our results. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions.

References

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