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.


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.