Stability of solution of a backward problem of a time-fractional diffusion equation with perturbed order

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.