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Regularization of a terminal value problem for time fractional diffusion equation

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2020

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Open Access Color

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Abstract

In this article, we study an inverse problem with inhomogeneous source to determine an initial data from the time fractional diffusion equation. In general, this problem is ill-posed in the sense of Hadamard, so the quasi-boundary value method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them. Finally, two numerical results in the one-dimensional and two-dimensional case show the evidence of the used regularization method.

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Keywords

Fractional Diffusion Equation, Inverse Problem, Regularization, Riemann-Lioville Fractional Derivative

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Citation

Triet, Nguyen Anh...et al. (2020). "Regularization of a terminal value problem for time fractional diffusion equation", Mathematical Methods in the Applied Sciences, Vol. 43, No. 6, pp. 3850-3878.

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Mathematical Methods in the Applied Sciences

Volume

43

Issue

6

Start Page

3850

End Page

3878