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Identifying the Fractional Orders in Anomalous Diffusion Models from Real Data

by Moreno Concezzi 1 and Renato Spigler 1,2,3,*
1
Department of Mathematics and Physics, Roma Tre University, 1, Largo S. Leonardo Murialdo, 00146 Rome, Italy
2
Faculty of Engineering, International Telematic University UNINETTUNO, 00186 Rome, Italy
3
Institute for the Applications of Computing, Italian National Research Council, 00185 Rome, Italy
*
Author to whom correspondence should be addressed.
Fractal Fract 2018, 2(1), 14; https://doi.org/10.3390/fractalfract2010014
Received: 10 October 2017 / Revised: 8 February 2018 / Accepted: 15 February 2018 / Published: 24 February 2018
(This article belongs to the Special Issue Fractional Dynamics)
An attempt is made to identify the orders of the fractional derivatives in a simple anomalous diffusion model, starting from real data. We consider experimental data taken at the Columbus Air Force Base in Mississippi. Using as a model a one-dimensional fractional diffusion equation in both space and time, we fit the data by choosing several values of the fractional orders and computing the infinite-norm “errors”, representing the discrepancy between the numerical solution to the model equation and the experimental data. Data were also filtered before being used, to see possible improvements. The minimal discrepancy is attained correspondingly to a fractional order in time around 0 . 6 and a fractional order in space near 2. These results may describe well the memory properties of the porous medium that can be observed. View Full-Text
Keywords: inverse problems; anomalous diffusion; fractional differential equations inverse problems; anomalous diffusion; fractional differential equations
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Concezzi, M.; Spigler, R. Identifying the Fractional Orders in Anomalous Diffusion Models from Real Data. Fractal Fract 2018, 2, 14.

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