Stable numerical solution of a fractional-diffusion inverse heat conduction problem

The ill-posed problem of attempting to recover the boundary temperature and the heat flux functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed. A simple algorithm based on space marching mollification techniques is introduced for the numerical solution of the discrete problem. Stability bounds, error estimates and numerical examples of interest are also presented.