Non-classical Regularization Methods For The Inverse Problems Of A Time-space Fractional Diffusion Equation

In this paper,we consider a backward problem with a fractional Laplacian and fractional time derivative.We propose two regularization methods,i.e.the truncation method and the fractional Tikhonov regularization method,and give the a-priori and Morozov parameter choice rules,respectively.This paper shows the stability estimate and error estimate under the two regularization parameter choice rules.Finally,several examples are conducted to illustrate the effectiveness of the two regularization methods.