Approximate controllability results for nonlocal impulsive functional integro-differential systems through fractional operators
This paper is concerned with a class of first-order nonlocal impulsive functional integro-differential equations with $\al$-norm in Banach spaces. We assume that the linear part generates an analytic compact bounded semigroup, and that the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part. Sufficient conditions for existence and approximate controllability of mild solutions are obtained by using the theory of fractional operators, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. Finally, an example is provided to illustrate the obtained abstract results.