AIMS Mathematics, 2020, 5(1): 259-272. doi: 10.3934/math.2020017.

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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

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 Mönch’s 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.
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Keywords fractional differential equation; fractional integral conditions; Caputo-Hadamard fractional derivative; Kuratowski measures of noncompactness; Mönch fixed point theorems; Banach space

Citation: Abdelatif Boutiara, Kaddour Guerbati, Maamar Benbachir. Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces. AIMS Mathematics, 2020, 5(1): 259-272. doi: 10.3934/math.2020017

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