Existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators Original Research Article

This paper is mainly concerned with existence of mild solutions for a first order impulsive neutral integrodifferential inclusions with nonlocal initial conditions in αα-norm. We assume that the linear part generates an analytic semigroup and transform it into an integral inclusion. By using a fixed point theorem for multi-valued maps due to Dhage, a main existence theorem is established. Finally, we present an example to illustrate this main theorem.