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

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

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

Author(s) -

Adel Lachouri,

Mohammed S. ‬Abdo,

Abdelouaheb Ardjouni,

Bahaaeldin Abdalla,

Thabet Abdeljawad

Publication year - 2021

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 15

ISSN - 2473-6988

DOI - 10.3934/math.2022193

Subject(s) - mathematics , fractional calculus , class (philosophy) , frame (networking) , operator (biology) , pure mathematics , nonlinear system , mathematical analysis , regular polygon , differential inclusion , convex function , fixed point theorem , fixed point , partial derivative , differential (mechanical device) , geometry , physics , computer science , telecommunications , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , transcription factor , gene , thermodynamics

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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