Eur. Phys. J. Plus (2019) 134: 217
https://doi.org/10.1140/epjp/i2019-12554-9

Regular Article

Fractional Rényi entropy^⋆

¹ Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal
² UISPA - LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

^* e-mail: aml@fe.up.pt

Received: 2 January 2019
Accepted: 2 February 2019
Published online: 22 May 2019

Abstract

This paper proposes two novel expressions for the Rényi entropy inspired in the concepts of fractional calculus. The new formulations are applied to the Bernoulli distribution, the Dow Jones Industrial Average time series and data from researcher citation profiles. The results are compared with those provided by other fractional entropies. The tuning by means of the fractional order allows a superior sensitivity of the entropy to the characteristics exhibited by each distinct type of data. Indeed, the additional freedom provided by the two parameters of the new Rényi formulations is useful when characterizing assertively real world data representative of complex systems.