Anomalous Diffusion with Caputo-Fabrizio Time Derivative: an Inverse Problem.
DOI:
https://doi.org/10.5540/tcam.2022.023.03.00515Keywords:
Inverse problems, fractional calculus, anomalous diffusionAbstract
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.
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