Anomalous Diffusion with Caputo-Fabrizio Time Derivative: an Inverse Problem. - Seminara, S. A.; Troparevsky, M. I.; Fabio, M. A.; La Mura, G. (Trends in Computational and Applied Mathematics, 2022)
In this work we approximate the source for a non homogeneous fractional diffusion equation in 1D, from measurements of the concentration at a finite number of points. We use Caputo-Fabrizio time fractional derivative to model anomalous diffusion. Separating variables, we arrive to a linear system which provides approximate values for the Fourier coefficients of the unknown source. Numerical examples show the efficiency of the method, as well as some of its practical limitations.