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 the Mönch fixed point theorem as well as the theory of fractional calculus and the ( α , β ) $(\alpha ,\beta )$ -resolvent operator, we concern with the term u ′ ( ⋅ ) $u'(\cdot )$ and finding a control v such that the mild solution satisfies u ( b ) = u b $u(b)=u_{b}$ and u ′ ( b ) = u b ′ $u'(b)=u'_{b}$ . Finally, we present an application to support the validity study.