The quasi-reversibility regularization method for backward problem of the multi-term time-space fractional diffusion equation

In this paper, we investigate a backward problem of 1D multi -term time-space fractional diffusion equation, which is ill -posed. With the help of quasi -reversibility regularization method, we give the regularization solution, based on some properties of Fourier transform and Mittag-Leffler functions. Besides, we establish a -priori and a -posteriori convergence estimates, respectively. Finally, we illustrate two numerical examples to verify the effectiveness and feasibility of our proposed method.