# American Institute of Mathematical Sciences

July  2019, 24(7): 3195-3210. doi: 10.3934/dcdsb.2018340

## Regularity of solutions to time fractional diffusion equations

 School of Mathematics, Sichuan University, Chengdu 610064, China

* Corresponding author: Xiaoping Xie, xpxie@scu.edu.cn

Received  June 2017 Revised  December 2017 Published  January 2019

Fund Project: This work was supported by National Natural Science Foundation of China (11771312) and Major Research Plan of National Natural Science Foundation of China (91430105).

We derive some regularity estimates of the solution to a time fractional diffusion equation by using the Galerkin method. The regularity estimates partially unravel the singularity structure of the solution with respect to the time variable. We show that the regularity of the weak solution can be improved by subtracting some particular forms of singular functions.

Citation: Binjie Li, Xiaoping Xie. Regularity of solutions to time fractional diffusion equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3195-3210. doi: 10.3934/dcdsb.2018340
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