Existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators

In this paper, by using the Leray–Schauder alternative, we have investigated the existence of mild solutions to first-order impulsive partial functional integrodifferential equations with nonlocal conditions in an αα-norm. 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. An example is also given to illustrate our main results.