Existence of solutions for neutral integrodifferential equations with nonlocal conditions

This paper is concerned with the existence of mild solutions, strong solutions and strict solutions for a class of neutral integrodifferential equations with nonlocal conditions in Banach space. Since the nonlinear terms of the systems involve spacial derivatives, the theory of fractional power and α-norm is used to discuss the problem. In the end an example is provided to illustrate the applications of the obtained results.