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Abstract

In the present paper, we consider a backward problem for a space-fractional diffusion equation (SFDE) with a time-dependent coefficient. Such the problem is obtained from the classical diffusion equation by replacing the second-order spatial derivative with the Riesz-Feller derivative of order α∈(0,2]. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Therefore, we propose one new regularization solution to solve it. Then, the convergence estimate is obtained under a priori bound assumptions for exact solution.



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Issue: Vol 1 No T5 (2017)
Page No.: 172-183
Published: Nov 29, 2018
Section: Original Research
DOI: https://doi.org/10.32508/stdjns.v1iT5.551

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Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Dinh, H. (2018). Regularization for a Riesz-Feller space fractional backward diffusion problem with a time-dependent coefficient. Science and Technology Development Journal - Natural Sciences, 1(T5), 172-183. https://doi.org/https://doi.org/10.32508/stdjns.v1iT5.551

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