Maximum principles for a time-space fractional diffusion equation

TL;DR

This paper establishes maximum principles for a comprehensive class of fractional diffusion equations involving both time and space derivatives, extending classical results to fractional operators.

Contribution

It introduces maximum principles for full fractional diffusion equations, including both time and space fractional derivatives, which were not previously available.

Findings

Maximum principles for classical solutions.

Maximum principles for weak solutions.

Extension to full fractional diffusion equations.

Abstract

In this paper, we focus on maximum principles of a time-space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using properties of the time fractional derivative operator and the fractional Laplace operator. We deduce maximum principles for a full fractional diffusion equation, other than time-fractional and spatial-integer order diffusion equations.