Eur. Phys. J. Plus (2017) 132: 36
https://doi.org/10.1140/epjp/i2017-11306-3

Regular Article

Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

¹ International College, Hunan University of Arts and Science, 415000, Changde, China
² School of Physics and Electronics, Central South University, 410083, Changsha, China

^* e-mail: heshaobo_123@163.com

Received: 24 October 2016
Accepted: 18 December 2016
Published online: 23 January 2017

Abstract

In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.