Existence Results for Fractional Integro-Differential Equations(FRIDE) with State-Dependent Delays and Infinite Delay in Frechet Spaces (FS)

Abstract

In this paper, we investigate the existence of mild solutions for semilinear integro-differential equations with state-dependent
delay of order 0 < b < 1 and infinite delay in Frechet spaces. We assume that the linear part possesses a resolvent operator. The ´
existence of mild solutions is established using Kuratowski’s measure of noncompactness and the generalized Darbo fixed point
theorem in Frechet spaces. Finally, an example is provided for demonstration.