Electron. J. Differential Equations, Vol. 2016 (2016), No. 290, pp. 1-18.

A regularization method for time-fractional linear inverse diffusion problems

Nguyen Huy Tuan, Mokhtar Kirane, Vu Cam Hoan Luu, Bandar Bin-Mohsin

In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results.

Submitted July 26, 2016. Published October 26, 2016.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Regularization method; inverse advection-dispersion problem; Caputo fractional derivatives; convergence estimate.

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Nguyen Huy Tuan
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Vietnam
email: nguyenhuytuan@tdt.edu.vn
Mokhtar Kirane
LaSIE, Faculté des Sciences
Pôle Sciences et Technologie
Universié de La Rochelle
Avenue M. Crépeau, 17042 La Rochelle Cedex, France
email: mokhtar.kirane@univ-lr.fr
Vu Cam Hoan Luu
Faculty of Basic Science
Posts and Telecommunications Institute of Technology
Ho Chi Minh City, Vietnam
email: lvcamhoan@gmail.com
Bandar Bin-Mohsin
Department of Mathematics
College of Sciences, King Saud University
Riyadh, Saudi Arabia
email: balmohsen@ksu.edu.sa

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