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On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator

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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