摘要：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 α x ( t ) = A x ( t ) + D t α − 1 F ( t , x ( t ) ) $D_{t}^{\alpha}x(t)=Ax(t)+D_{t}^{\alpha-1}F(t,x(t))$ , t ∈ R $t\in \mathbb{R}$ , where 1 < α < 2 $1<\alpha<2$ , A is a linear densely defined operator of sectorial type of ω < 0 $\omega<0$ 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.
关键词：weighted Stepanov-like pseudo-almost automorphic function ; semilinear fractional differential equation ; fractional relaxation-oscillation equation ; solution operator ; fractional integral
