Abstract: Firstly, by using Tikhonov regularization method to solve the inverse source problem of the fractional heat conduction equation with Riemann-Liouville derivative, we obtained a regularization solution with Mittag-Leffler function. Secondly, we analyzed the convergence of the regularization solution, gave the error estimate of the regularization and exact solutions under a priori parameter choice rule, and the range of regularization parameter under a posterior parameter choice rule. The numerical experiment results show the effectiveness of proposed regularization method.

Key words: fractional heat conduction equation, inverse source problem, Mittag-Leffler function, regularization method, error estimate