Existence and stability of solutions to neutral equations with infinite delay

In this article, by using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and αnorm is used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. A stability result for the autonomous case is also established. We conclude with an example that illustrates the applications of the results obtained.