On some classes of almost automorphic functions and applications to fractional differential equations
We study in this paper the properties of C(n) C ( n ) -almost automorphic and asymptoticallyC(n) C ( 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 D?x(t)=Ax(t)+F(t,x(t),Bx(t)) D ? x ( t ) = A x ( t ) + F ( t , x ( t ) , B x ( t ) ) with t?R,0<?<1 t ? R , 0 < ? < 1 , where A A generates a family of ? ? -resolvent family S?(t) S ? ( t ) and f f satisfies some Lipschitz conditions.
fractional differential equation c(n) c ( n ) -almost automorphic functions c(n) c ( n ) c(n) c ( n ) c ( n ) asymptotically almost automorphic functions