A study on controllability of impulsive fractional evolution equations via resolvent operators

Abstract In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on Mönch fixed point theorem as well theory of calculus and $(\alpha ,\beta )$ ( α , β ) -resolvent operator, concern with term $u'(\cdot u ′ ⋅ finding control v such that mild solution satisfies $u(b)=u_{b}$ b = $u'(b)=u'_{b}$ . Finally, present an application to support validity study.