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

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.


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