Existence and regularity of strict solutions for a class of fractional evolution equations

Abstract

We study the existence and Hölder regularity of solutions for fractional evolution equations of order $\alpha \in (1,2)$. By means of an analytic resolvent, we construct an interpolation space, which can effectively lower the regularity of initial data. By virtue of the interpolation space and some properties of the analytic resolvent, we derive the existence and Hölder regularity of strict solutions for an inhomogeneous problem, as well as the existence and Hölder regularity of a nonlinear problem.