Existence Results for Semilinear Fractional Functional Differential Equations with State-Dependent Delay

Abstract

According to theories for α-resolvent family (S_α(t))t≥0 and fixed point methods, this paper is mainly concerned with existence of mild solutions to a semilinear fractional functional differential equation with state-dependent delay in a complex Banach space X. Some sufficient conditions are established without the compactness of (S_α(t))_t≥0.