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Entropy 2018, 20(5), 384; https://doi.org/10.3390/e20050384

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

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.
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)

Abstract

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 β -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 β -conformable attractors are provided to illustrate the effectiveness of the proposed method. View Full-Text
Keywords: fractional calculus; fractional conformable derivative; fractional β-conformable derivative; chaos; Adams–Moulton scheme fractional calculus; fractional conformable derivative; fractional β-conformable derivative; chaos; Adams–Moulton scheme
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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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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