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A Review of Fractional Order Entropies

LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(12), 1374;
Received: 11 November 2020 / Revised: 26 November 2020 / Accepted: 2 December 2020 / Published: 5 December 2020
(This article belongs to the Special Issue Review Papers for Entropy)
Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful. View Full-Text
Keywords: fractional calculus; entropy; information theory fractional calculus; entropy; information theory
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MDPI and ACS Style

Lopes, A.M.; Machado, J.A.T. A Review of Fractional Order Entropies. Entropy 2020, 22, 1374.

AMA Style

Lopes AM, Machado JAT. A Review of Fractional Order Entropies. Entropy. 2020; 22(12):1374.

Chicago/Turabian Style

Lopes, António M., and José A.T. Machado 2020. "A Review of Fractional Order Entropies" Entropy 22, no. 12: 1374.

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