Anomalous Diffusion with Caputo-Fabrizio Time Derivative: an Inverse Problem.

In this work we approximate the source for a non homogeneous fractionaldiffusion equation in 1D, from measurements of the concentration at a finite number ofpoints. We use Caputo-Fabrizio time fractional derivative to model anomalous diffusion.Separating variables, we arrive to a linear system which provides approximate values forthe Fourier coefficients of the unknown source. Numerical examples show the efficiency ofthe method, as well as some of its practical limitations.