On an inverse problem for tempered fractional diffusion equation

Abstract

In this paper, we consider the tempered fractional diffusion equation with integral condition. We give the two main results. The first results concerns on the well-posedness of the mild solution and provide some estimates on upper bound and lower bound for the solution. We also investigate the continuity results for fractional order of the solution. The second result is the regularization of the inverse problem.
The first method is based on the quasi-reversibility method and we give the error estimate in $L^2$ spaces. For the second regularized solution, we apply the Fourier truncation method. We obtain the error estimates in the higher spaces $\mathbb H^s$.