Existence and Regularity of solutions in alpha norm for some second order partial neutral functional differential equations in Banach Spaces

Abstract

The purpose of this paper is to study the existence and regularity of solutions in the $\alpha$-norm for  some second order partial neutral functional differential equations with finite delay in Banach spaces. To do this, we use the cosine family theory and Schauder's fixed point Theorem to establish the local existence of solutions and we give some sufficients conditions to enssure the regularity of solutions. Finally, we give an example to illustrate the theoretical results.