S‐Asymptotically Periodic Solutions for Fractional Evolution Equation With Deviated Argument

This work is devoted to the existence of an ‐asymptotically periodic solution for an abstract fractional evolution equation involving the Caputo derivative and a fractional power operator. The existence and global asymptotic behavior of the ‐asymptotically periodic solution are established using fixed point theorem, an exponentially stable compact semigroup, and certain appropriate inequalities. An example is provided demonstrating the application of the abstract results.