Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors
by
Jesús Emmanuel Solís Pérez 1,
José Francisco Gómez-Aguilar 2,*
,
Dumitru Baleanu 3,4 and
Fairouz Tchier 5
Jesús Emmanuel Solís Pérez 1,
José Francisco Gómez-Aguilar 2,*,
Dumitru Baleanu 3,4 and
Fairouz Tchier 5
1
Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico
2
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico
3
Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey
4
Institute of Space Sciences, P.O. Box, MG-23, R 76900 Magurele-Bucharest, Romania
5
Department of Mathematics, King Saud University, P.O. BOX 2454, Riyadh 11451, Saudi Arabia
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(5), 384; https://doi.org/10.3390/e20050384
Received: 28 February 2018 / Revised: 27 April 2018 / Accepted: 8 May 2018 / Published: 20 May 2018
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich–Fabrikant, Thomas’ cyclically symmetric attractor and Newton–Leipnik. Fractional conformable and -conformable derivatives of Liouville–Caputo type are considered to solve the proposed systems. A numerical method based on the Adams–Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and -conformable attractors are provided to illustrate the effectiveness of the proposed method.
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Keywords:
fractional calculus; fractional conformable derivative; fractional β-conformable derivative; chaos; Adams–Moulton scheme
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MDPI and ACS Style
Pérez, J.E.S.; Gómez-Aguilar, J.F.; Baleanu, D.; Tchier, F. Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors. Entropy 2018, 20, 384.
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