Existence and regularity of solutions for neutral partial integro-differential equations with nonlocal conditions

In this work, we study the existence of mild and classical solutions for neutral partial functional integro-differential equations with non-local condition. We discuss the problems by making full use of resolvent operators theory newly established in the literature, theory of fractional power, α-norm and Schauder’s fixed point theorem. Some results on existence and regularity of solutions of the considered equation are obtained. Finally, an example is presented to illustrate the obtained results.