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Open AccessArticle

An Entropy Formulation Based on the Generalized Liouville Fractional Derivative

1
Grupo Física-Matemática, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1649-003 Lisboa, Portugal
2
Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. 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 2019, 21(7), 638; https://doi.org/10.3390/e21070638
Received: 15 June 2019 / Revised: 21 June 2019 / Accepted: 25 June 2019 / Published: 28 June 2019
(This article belongs to the Special Issue The Fractional View of Complexity)
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PDF [368 KB, uploaded 28 June 2019]
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Abstract

This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series. View Full-Text
Keywords: fractional derivatives; fractional calculus; entropy fractional derivatives; fractional calculus; entropy
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Ferreira, R.A.C.; Tenreiro Machado, J. An Entropy Formulation Based on the Generalized Liouville Fractional Derivative. Entropy 2019, 21, 638.

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