The authors consider the existence of solutions of the neutral partial differential equation with nonlocal conditions:
where generates an analytic compact semigroup on a Banach space and where the functions , and satisfy specific continuity and measurability constraints. Fractional powers of are used. By the fixed point theorem of Sadovskii existence of a mild solution is obtained. When is a reflexive Banach space and is Lipschitz continuous, a strong solution is obtained. The results are applied to a class of partial differential equations with nonlocal conditions.