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

ABSTRACT

In this work we identify the source in a 1D anomalous diffusion equation, from measurements of the concentration at a finite number of points. We use Caputo-Fabrizio time fractional derivative to model the phenomenon. 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.

Keywords:
inverse problems; fractional calculus; anomalous diffusion