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On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

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2020

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Open Access Color

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Abstract

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L-2 and H-tau norms is considered and illustrated by numerical example.

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Backward Problem, Fractional Diffusion Equation, Random Noise, Regularized Solution

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Citation

Tuan, Nguyen Huy...et al. (2019). "On a backward problem for fractional diffusion equation with Riemann-Liouville derivative", Mathematical Methods in the Applied Sciences, Vol. 43, No. 3, pp. 1292-1312.

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Mathematical Methods in the Applied Sciences

Volume

43

Issue

3

Start Page

1292

End Page

1312