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

S. A. Seminara, M. I. Troparevsky, M. A. Fabio, G. La Mura


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.


Inverse problems, fractional calculus, anomalous diffusion

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