On almost automorphic mild solutions for fractional semilinear initial value problems

This paper investigates almost automorphic mild solutions of the fractional semilinear equation D x.t/ D Ax.t/ C f .t; x.t//; 0 < < 1, considered in a Banach space X, where A is a linear operator of sectorial type ! < 0. Some sufficient conditions are given for the existence, uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation.