Abstract
In this paper, we study the solvability and optimal controls of a class of fractional integrodifferential evolution systems with infinite delay in Banach spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence and continuous dependence of mild solutions are investigated by utilizing the techniques of a priori estimation and extension of step by steps. Finally, existence of optimal controls for system governed by fractional integrodifferential evolution systems with infinite delay is proved.