Research Article Almost Automorphic Solutions to Abstract Fractional Differential Equations

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation Dαt ut Aut D α−1 t ft, ut 1 < α < 2, in complex Banach spaces, with Stepanov-like almost automorphic coefficients. Moreover, an application to a fractional relaxation-oscillation equation is given. 1