New results for infinite functional differential inclusions with impulses effect and sectorial operators in Banach spaces

Year 2021, Volume: 5 Issue: 3, 382 - 392, 30.09.2021

Nawal Alsarori Kirtiwant Ghadle

https://doi.org/10.31197/atnaa.844234

Abstract

This article aims to use Bohnenblust Karlin’s fixed point theorem to obtain new results for the impulsive
inclusions with infinite delay in Banah space given by the form
(P)
8><
>:
cD®
t x(t )¡ Ax(t ) 2 F(t ,xt ), t 2 J , t 6Æ ti ,
¢x(ti ) Æ Ii (x(t¡
i )), i Æ 1, ...,m,
x(t ) ƪ(t ), t 2 (¡1,0].
where cD® is theCaputo derivative. We examine the casewhen themultivalued function F is an upperCarathéodory
and the linear part is sectorial operator defined on Banach space. Also, we provide an example to elaborate the
outcomes.

Keywords

Fractional impulsive differential inclusions, Nonlocal conditions, Fixed point theorems

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