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Abstract

The aim of this paper is of studying the stability of solution of a backward problem of a timefractional diffusion equation with perturbed order. We investigate the well-posedness of the backward problem with perturbed order for t>0. The results on the unique existence and continuity with respect to the fractional order, the source term as well as the final value of the solution are given. At t=0 the backward problem is ill-posed and we introduce a truncated method to regularize the backward problem with respect to inexact fractional order. Some error estimates are provided in Holder type.


 



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Issue: Vol 22 No 1 (2019)
Page No.: 158-164
Published: Mar 29, 2019
Section: Natural Sciences - Research article
DOI: https://doi.org/10.32508/stdj.v22i1.1222

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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
Dien, N., & Trong, D. (2019). Stability of solution of a backward problem of a time-fractional diffusion equation with perturbed order. Science and Technology Development Journal, 22(1), 158-164. https://doi.org/https://doi.org/10.32508/stdj.v22i1.1222

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