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Entropy 2014, 16(4), 2350-2361; doi:10.3390/e16042350

Fractional Order Generalized Information

Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
Received: 3 April 2014 / Revised: 16 April 2014 / Accepted: 21 April 2014 / Published: 24 April 2014
(This article belongs to the Special Issue Complex Systems and Nonlinear Dynamics)
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This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.
Keywords: information; entropy; fractional calculus information; entropy; fractional calculus
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Machado, J.T. Fractional Order Generalized Information. Entropy 2014, 16, 2350-2361.

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