Existence results for neutral integro-differential equations with nonlocal conditions

Abstract

We study the existence and regularity of solutions for neutral integro-differential equations with nonlocal condition by applying the theory of resolvent operators established recently in the literature. Since the nonlinear terms of the systems involve spacial derivatives, we make full use of the theory of fractional power, the $\alpha$-norm, and Schauder’s fixed point theorem to discuss the problems. An example is given to illustrate the applications of the obtained results.