Optimal results for a time-fractional inverse diffusion problem under the Hölder type source condition

‎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.