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An inverse problem for an inhomogeneous time-fractional diffusion equation: a regularization method and error estimate

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Abstract

In this paper, we study an inverse problem for an inhomogeneous time-fractional diffusion equation in the one-dimensional real-positive semiaxis domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. After we show that the inverse problem is severely ill posed, we apply a modified regularization method based on the solution in the frequency domain to solve the inverse problem. A convergence estimate is also derived. We present two numerical examples to show the efficiency of the method.

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Acknowledgements

The authors thank the referee for his/her very careful reading and for pointing out several mistakes as well as for the useful comments and suggestions.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Huy Tuan

  2. Faculty of Basic Science, Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam

    Luu Vu Cam Hoan

  3. Department of Mathematics and Computer Science, University of Science-VNU.HCMC, Ho Chi Minh City, Vietnam

    Luu Vu Cam Hoan

  4. Department of Mathematics and Computer Science, Alfaisal University, Riyadh, Saudi Arabia

    Salih Tatar

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  1. Nguyen Huy Tuan
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  2. Luu Vu Cam Hoan
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  3. Salih Tatar
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Correspondence to Salih Tatar.

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Communicated by Domingo Alberto Tarzia.

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Tuan, N.H., Hoan, L.V.C. & Tatar, S. An inverse problem for an inhomogeneous time-fractional diffusion equation: a regularization method and error estimate. Comp. Appl. Math. 38, 32 (2019). https://doi.org/10.1007/s40314-019-0776-x

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  • DOI: https://doi.org/10.1007/s40314-019-0776-x

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