### An inverse problem for homogeneous time-fractional diffusion problem on the sphere

Document Type : Research Paper

Author

Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

Abstract

In this paper, we consider an inverse problem for the time-fractional diffusion equation on the sphere where the final data on the sphere are given. The problem is ill-posed in the sense of Hadamard. Hence, the regularization method has to be used for the stable approximate solution. Then the well-posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one is proved. Error estimates for this method are provided together with a selection rule for the regularization parameter.

Keywords

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###### Volume 12, Special IssueDecember 2021Pages 653-662
• Receive Date: 27 May 2020
• Revise Date: 09 August 2020
• Accept Date: 20 August 2020