Asymptotic periodicity for a class of fractional integro--differential equations

In this paper, we are concerned with the existence and uniqueness of S-asymptotically ω-periodic solutions to a class of fractional integro-differential equations. Some sufficient conditions are established about the existence and uniqueness of S-asymptotically ω-periodic solutions to the fractional integro-differential equation by applying fixed point theorem combined with sectorial operator, where the nonlinear perturbation term f is a Lipschitz case and non-Lipschitz case.