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

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.