Open AccessExistence and stability of solutions of $ \psi $-Hilfer fractional functional differential inclusions with non-instantaneous impulses
Author(s) -
Ahmed Ibrahim,
A. A. Elmandouh
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021628
Subject(s) - mathematics , stability (learning theory) , mathematical analysis , operator (biology) , fractional calculus , differential inclusion , differential equation , pure mathematics , computer science , biochemistry , chemistry , repressor , machine learning , transcription factor , gene
In this paper, we prove two existence results of solutions for an $ \psi $-Hilfer fractional non-instantaneous impulsive differential inclusion in the presence of delay in an infinite dimensional Banah spaces. Then, by using the multivalued weakly Picard operator theory, we study the stability of solutions for the considered problem in the sense of $ \psi $-generalized Ulam-Hyers. To achieve our aim, we present a relation between any solution of the considered problem and the corresponding fractional integral equation. The given problem here is new because it contains a delay and non-instantaneous impulses effect. Examples are given to clarify the possibility of applicability our assumptions.