Classical Solutions to the Initial-Boundary Value Problems for Nonautonomous Fractional Diffusion Equations

Abstract EN

In this paper, we investigate a class of nonautonomous fractional diffusion equations (NFDEs).

Firstly, under the condition of weighted Hölder continuity, the existence and two estimates of classical solutions are obtained by virtue of the properties of the probability density function and the evolution operator family.

Secondly, it focuses on the continuity and an estimate of classical solutions in the sense of fractional power norm.

The results generalize some existing results on classical solutions and provide theoretical support for the application of NFDE.