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

Jesús Emmanuel Solís Pérez; José Francisco Gómez-Aguilar; Dumitru Baleanu; Fairouz Tchier

doi:10.3390/e20050384

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

Entropy (Basel). 2018 May 20;20(5):384. doi: 10.3390/e20050384.

Authors

Jesús Emmanuel Solís Pérez¹, José Francisco Gómez-Aguilar², Dumitru Baleanu^{3

4}, Fairouz Tchier⁵

Affiliations

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.

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.

Keywords: Adams–Moulton scheme; chaos; fractional calculus; fractional conformable derivative; fractional β-conformable derivative.