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<p/> <p>A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation <inline-formula><graphic file="1687-1847-2010-508374-i1.gif"/></inline-formula>, in complex Banach spaces, with <it>Stepanov-like almost automorphic coefficients</it>. Moreover, an application to a fractional relaxation-oscillation equation is given.</p>