Pseudo S-asymptotically Bloch type periodic solutions to fractional integro-differential equations with Stepanov-like force terms

In this paper, we firstly present some notions of Stepanov-like S-asymptotically (omega, k)-Bloch periodic function, Stepanov-like (weighted) pseudo S-asymptotically (omega, k)-Bloch periodic functions and establish some basic properties of such functions. Finally, we investigate the existence and uniqueness of pseudo S-asymptotically (omega, k)-Bloch periodic solutions to a fractional integro-differential equation in Banach spaces with a Stepanov-like force function. The obtained results show that for each pseudo S-asymptotically (omega, k)-Bloch periodic input via Stepanov-like forcing disturbance, the output remains to be a bounded continuous mild solutions to the reference equation, which is also pseudo S-asymptotically (omega, k)-Bloch periodic.