On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
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Date
2020
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Abstract
In this paper, we consider an inverse problem of recovering the initial value for a generalization of time-fractional diffusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.
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Fractional Tikhonov Regularization, Hyper-Bessel Operator, Time-Fractional Diffusion Equation
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Citation
Tuan, Nguyen Huy...et al. (2020). "On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator", Mathematical Methods in the Applied Sciences, Vol. 43, No. 6, pp. 2858-2882.
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Mathematical Methods in the Applied Sciences
Volume
43
Issue
6
Start Page
2858
End Page
2882