Document Type: Research Paper
School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, P. R. China
In the present paper we consider a time-fractional inverse diffusion problem, where data is given at $x=1$ and the solution is required in the interval $0<x<1$. This problem is typically ill-posed: the solution (if it exists) does not depend continuously on the data. We give the optimality analysis for this problem, and an optimal regularization method is also provided. Numerical examples show that this method works effectively.