On S‐asymptotically ω‐periodic and Bloch periodic mild solutions to some fractional differential equations in abstract spaces

Abstract

We are concerned with the existence and uniqueness of S‐asymptotically ω‐periodic and Bloch periodic mild solutions to the semilinear fractional differential equation of the form where is the Riemann‐Liouville derivative, 1 < α < 2 and A is a (generally unbounded) linear operator, which generates a bounded α‐resolvent family Tα(t) on a (complex) Banach space X. We use some classical fixed‐point theorems to reach our results. The results are new even in the context of asymptotically periodic solutions.