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

#### Abstract

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.

#### Keywords

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DOI: https://doi.org/10.5540/tcam.2022.023.03.00515

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