Weighted Pseudo Antiperiodic Solutions for Fractional Integro-Differential Equations in Banach Spaces

Abstract In this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro-differential equations in the form (Formula presented.),where f(·,u(·)) is Stepanov-like weighted pseudo antiperiodic and A generates a resolvent family of bounded and linear operators on a Banach space X,a ∈ Lloc1(ℝ+) and α>0. Here the fractional derivative is considered in the sense of Weyl. Also, we give a short proof to show that the vector-valued space of Stepanov-like weighted pseudo antiperiodic functions is a Banach space. © 2015 Elsevier Inc. All rights reserved.