On some classes of almost automorphic functions and applications to fractional differential equations

AbstractWe study in this paper the properties of C(n)-almost automorphic and asymptoticallyC(n)-almost automorphic functions (a new concept) with values in a Banach space. We then give a new result related to the existence and uniqueness of an asymptotically almost automorphic solution of a semilinear fractional differential equation of the form Dαx(t)=Ax(t)+F(t,x(t),Bx(t)) with t∈R,0<α