Weighted pseudo almost automorphic solution of an integro-differential equation, with weighted Stepanov-like pseudo almost automorphic forcing term

摘要

In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution of an integrodifferential equation (with weighted Sp-pseudo almost automorphic forcing term) in a Banach space X. We use fractional powers of operators and the Banach fixed point theorem in order to obtain our result. Very recently introduced concept of "weighted ~(Sp)-pseudo almost automorphy" has been used here.