On fractional semilinear nonlocal initial value problem with state dependent delay (Q6568961)

The authors study a class of fractional order semilinear abstract Cauchy problem with state dependent delay subject to nonlocal initial conditions. They are interested in the existence of Hölder classical solution and mild solution solutions of such equations. They used Krasnoselskii's fixed point theorem with suitable assumptions for the first type of solutions, and Schauder's fixed point theorem with suitable assumptions to obtain the second type of solutions.