Abstract
In this article, we deal with the existence of S-asymptotically omega-periodic mild solutions of Hilfer fractional evolution equations. We also investigate the Ulam-Hyers and Ulam-Hyers-Rassias stability of similar solutions. These results are established in Banach space with the help of resolvent operator functions and fixed point technique on an unbounded interval . An example is also presented for the illustration of obtained results.