Abstract This paper applies the Euler and the fourth-order Runge–Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov exponent is obtained based on the Euler method and applied with the Lorenz fractional attractor.

中文翻译：

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FDE 和符号包的 Euler 和 Runge-Kutta 广义方法在一些分数吸引子分析中的应用

摘要 本文将欧拉和四阶龙格-库塔方法应用于分数阶动力系统的分析。为了说明这两种技术，数值算法被应用于几个分数吸引子的解，即洛伦兹、达芬和刘系统。这些算法是在 Mathematica 符号包的帮助下实现的。此外，Lyapunov 指数是基于欧拉方法获得的，并与洛伦兹分数吸引子一起应用。