Weighted Stepanov-like pseudo-almost automorphic mild solutions for semilinear fractional differential equations

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D(t)(alpha)x(t) = Ax(t) + D-t(alpha-1) F(t, x(t)), t is an element of R, where 1 < alpha < 2, A is a linear densely defined operator of sectorial type of omega < 0 on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation.