## 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 language | English (US) |
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Title of host publication | Proceedings of the 2012 13th International Carpathian Control Conference, ICCC 2012 |

Pages | 458-463 |

Number of pages | 6 |

DOIs | |

State | Published - Jul 30 2012 |

Event | 2012 13th International Carpathian Control Conference, ICCC 2012 - High Tatras, Slovakia Duration: May 28 2012 → May 31 2012 |

### Other

Other | 2012 13th International Carpathian Control Conference, ICCC 2012 |
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Country | Slovakia |

City | High Tatras |

Period | 5/28/12 → 5/31/12 |

## Keywords

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

## ASJC Scopus subject areas

- Control and Systems Engineering