Semilinear Functional Differential Equations of Fractional order with State-Dependent Delay

In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon-Granas type for contractions maps in Frechet spaces combined with $\alpha$-resolvent family is the main tool in our analysis.