A note on an iterative algorithm for solving an inverse problem for a fractional-order partial differential equation

We consider an ill-posed inverse problem for a fractional-order partial differential equation (PDE). For its solution, we establish an iterative algorithm based on a sequence of well-posed problems previously developed for classical (non-fractional) elliptic and parabolic PDEs. For exact data, we prove the convergence of the algorithm and we establish its rate of the convergence. As with any regularising algorithm, in case of noisy data the iterations have to be stopped at an appropriate threshold before the solution's instability starts to manifest.