Existence of an Asymptotically Almost Periodic Solution for a Fractional Semilinear Problem

In this research, we consider that the fractional semilinear problem in sequentially compact Banach space , , with initial condition , , where is a generator of evolution system and is a given function satisfying some assumptions, has an asymptotically almost periodic solution. So, we consider a fractional semilinear integro-differential equation and we examine that this equation has an asymptotically almost periodic solution.