Spectral entropy in a fractional order model of anomalous diffusion

Richard L. Magin*, Carson Ingo

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Fractional order dynamic models of complex systems provide improved fits to experimental data with a reduced mean-squared error. The success of this approach, however, is dependent on the order of the derivatives included in the model. Fractional order models, for example, work better in describing the electrical and mechanical properties of multi-scale, heterogeneous materials than do integer order models. In order to estimate a measure of the expected improvement provided by fractional order models, we calculate the spectral entropy for anomalous diffusion as governed by the generalized diffusion equation in space and time. This fractional order representation of diffusion gives a minimum spectral entropy for Gaussian diffusion and predicts an increasing spectral entropy for non-Gaussian, or fractional, diffusion.

Original languageEnglish (US)
Title of host publicationProceedings of the 2012 13th International Carpathian Control Conference, ICCC 2012
Pages458-463
Number of pages6
DOIs
StatePublished - Jul 30 2012
Event2012 13th International Carpathian Control Conference, ICCC 2012 - High Tatras, Slovakia
Duration: May 28 2012May 31 2012

Other

Other2012 13th International Carpathian Control Conference, ICCC 2012
CountrySlovakia
CityHigh Tatras
Period5/28/125/31/12

Keywords

  • anomalous diffusion
  • complex systems
  • entropy
  • fractional derivative
  • information theory

ASJC Scopus subject areas

  • Control and Systems Engineering

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