On a class of differential inclusions in the frame of generalized Hilfer fractional derivative

Adel Lachouri; Mohammed S. Abdo; Abdelouaheb Ardjouni; Bahaaeldin Abdalla; Thabet Abdeljawad; Adel Lachouri; Mohammed S. Abdo; Abdelouaheb Ardjouni; Bahaaeldin Abdalla; Thabet Abdeljawad

doi:10.3934/math.2022193

AIMS Mathematics

2022, Volume 7, Issue 3: 3477-3493. doi: 10.3934/math.2022193

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On a class of differential inclusions in the frame of generalized Hilfer fractional derivative

1.
Applied Mathematics Lab, Department of Mathematics, Annaba University, P.O. Box 12, Annaba 23000, Algeria
2.
Department of Mathematics, Hodeidah University, P.O. Box 3114, Al-Hudaydah, Yemen
3.
Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras 41000, Algeria
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 25 September 2021 Accepted: 23 November 2021 Published: 02 December 2021
MSC : 34A08, 34A12, 34B15

In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the $ \varphi $-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a $ \varphi $-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.
- fractional differential inclusions,
- $ \varphi $-Hilfer fractional derivative,
- existence,
- fixed point theorem
Citation: Adel Lachouri, Mohammed S. Abdo, Abdelouaheb Ardjouni, Bahaaeldin Abdalla, Thabet Abdeljawad. On a class of differential inclusions in the frame of generalized Hilfer fractional derivative[J]. AIMS Mathematics, 2022, 7(3): 3477-3493. doi: 10.3934/math.2022193

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Abstract

In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the $ \varphi $-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a $ \varphi $-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.

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