Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations

This paper is concerned with the existence and uniqueness of a weighted pseudo almost automorphic mild solution to the semilinear fractional equation: Dtαu(t)=Au(t)+Dtα−1f(t,u(t)),t∈R,1<α<2 in complex Banach spaces with SpSp-weighted pseudo almost automorphic coefficients, where AA is a linear densely defined operator of sectorial type on a complex Banach space XX. Moreover, we present an application to a fractional wave equation.