A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation D t α u ( t ) = A u ( t ) + D t α − 1 f ( t , u ( t ) )     ( 1 < α < 2 ) , in complex Banach spaces, with Stepanov-like almost automorphic coefficients . Moreover, an application to a fractional relaxation-oscillation equation is given.