Periodic Solutions andS-Asymptotically Periodic Solutions to Fractional Evolution Equations

Abstract

This paper deals with the existence and uniqueness of periodic solutions,S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.