On almost automorphic mild solutions for fractional semilinear initial value problems

This paper investigates almost automorphic mild solutions of the fractional semilinear equation Dαx(t)=Ax(t)+f(t,x(t)),0<α<1Dαx(t)=Ax(t)+f(t,x(t)),0<α<1, considered in a Banach space XX, where AA is a linear operator of sectorial type ω<0ω<0. Some sufficient conditions are given for the existence, uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation.