Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators

This paper is mainly concerned with existence of mild solutions for the first order impulsive neutral differential and integrodifferential equations with nonlocal initial conditions in α -norm. We assume that the linear part generates an analytic semigroup and transform them into suitable integral equations. By using a fixed point theorem for condensing maps, some existence theorems are established. As applications of these main theorems, some practical consequences are derived. Particularly, our results cover the cases where the function F takes values in different spaces such as X α and X μ . Finally, an example is also given to illustrate the obtained results.