Pseudo-almost periodic solutions of a class of semilinear fractional differential equations

Abstract

We study existence and uniqueness of a pseudo-almost periodic (of class infinity) mild solution to the semilinear fractional equation \(\partial_{t}^{\alpha}u=Au+\partial_{t}^{\alpha-1}f(\cdot,u),1<\alpha<2\), where A is a linear operator of sectorial negative type.