Open AccessOn a class of differential inclusions in the frame of generalized Hilfer fractional derivative
Author(s) -
Jamshed Nasir,
AUTHOR_ID,
Shahid Qaisar,
Saad Ihsan Butt,
Hassen Aydi,
M. De La Sen,
AUTHOR_ID,
AUTHOR_ID,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
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) , mathematical analysis , pure mathematics , nonlinear system , differential inclusion , partial derivative , convex function , fixed point theorem , regular polygon , boundary value problem , fixed point , geometry , computer science , physics , telecommunications , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , transcription factor , gene
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.