分数阶微积分的预估-校正算法及其应用

选用分数阶微分方程的预估-校正数值算法，对Chen混沌系统进行仿真研究．首先，讨论分数阶Chen混沌系统在一定的初始条件下，系统为混沌的并且仍然呈现出丰富和复杂的分数阶混沌动力学行为；然后，利用预估-校正数值计算方法，对分数阶Chen混沌系统方程进行离散化处理，得到系统方程组的离散化式；最后通过MATLAB软件进行计算，得到分数阶Chen混沌系统的仿真相图．根据初始状态变量的不同，得到相应混沌系统的仿真图．证明了分数阶预估-校正法可以很好地对分数阶系统方程进行数值稳定分析．

Predictor-Corrector Approach and Its Application for the Fractional-Order Calculus

Predictor-corrector approach was used for the numerical solution of fractional differential equations on Chen chaotic system. First, the fractional Chert chaotic system under certain initial conditions was discussed, the system is chaotic and still presents a rich and complex fractional order chaotic dynamics behavior. Then, the predictor-corrector approach for the numerical solution of fractional differential equations of fractional order discretization processing Chen chaotic system was also used to obtain the discretization equations of the system. Then MATLAB was used to get the fractional order Chen chaotic system simulation diagram. In accordance with the different variables, different simulation diagrams of chaotic system were obtained to improve the efficiency of the predictor-corrector approach to the numerical solution of fractional differential equations.