Natural Sciences - Research article
Stability of solution of a backward problem of a time-fractional diffusion equation with perturbed order
- Faculty of Natural Sciences, Thu Dau Mot University, Binh Duong, Vietnam
- Faculty of Math and Computer Science, University of Science, VNU-HCM
Correspondence to:
Nguyen Minh Dien,
Faculty of Natural Sciences, Thu Dau Mot University, Binh Duong, Vietnam.
Email:
diennm@tdmu.edu.vn.
Published:
2019-03-29
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.