Fractional functional differential equations with causal operators in Banach spaces

In this paper, we study the fractional functional differential equations with causal operators in an arbitrary separable Banach space. By means of the techniques of the measure of noncompactness, the existence and continuation of solutions are given. Further, some topological properties of solution sets are discussed and the existence of optimal solutions of the associated control problem are presented. An example is given to illustrate the result.