Almost Automorphic Solutions to Abstract Fractional Differential Equations. (2nd March 2010) - Ding, Hui-Sheng
Abstract : A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equationD 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.