Abstract
This article concerns the problem of reconstruction of the source term in a fractional diffusion equation from internal noisy measured data. The considered model corresponds to the two dimensional fractional spectral Laplacian differential equation. The inverse problem is reformulated as a minimization one and solved by applying a regularization technique to avoid numerical instabilities caused by the noisy perturbations of the measured data. We propose an efficient and accurate identification procedure inspired from the Landweber-type denoising algorithms. The efficiency of the proposed identification process is justified by some numerical investigations.