Absrtact: The calculation work of solving a fractional order differential system is huge since it relating to history.
摘 要：由于分数阶微分系统具有记忆功能，在其求解过程中计算量较大。
Combining fractional order differential theory with total variation method, a new image denoising model was proposed, which was based on fractional Partial Differential Equation (PDE).
将分数阶微分理论和全变分方法相结合应用于图像去噪，提出了一种基于分数阶偏微分方程的图像去噪新模型。
The analytical conditions that the fractional-order differential systems remain chaotic are obtained by analyzing the stability of the fixed points of the systems.
通过分析系统不动点的稳定性，得到分数阶微分系统存在混沌的解析条件。
Finally, some numerical examples are provided to show that the fractional order linear multiple step method for solving the fractional order ordinary differential equation is an effective method.
最后给出了一些数值例子，证实了这个分数阶线性多步法是解分数阶常微分方程的一个有效方法。
And the fractional -order chaotic system is very useful for security communication because it is a new chaotic system for its order is adjustable and the actual system usually is differential form.
另外，分数阶混沌系统是一类新型的混沌系统，其阶数可调使得它在复杂度上更优于整数阶混沌系统，同时，实际系统也通常以微分形式存在，因此分数阶混沌系统也很适用于保密通信。
And the fractional -order chaotic system is very useful for security communication because it is a new chaotic system for its order is adjustable and the actual system usually is differential form.
另外，分数阶混沌系统是一类新型的混沌系统，其阶数可调使得它在复杂度上更优于整数阶混沌系统，同时，实际系统也通常以微分形式存在，因此分数阶混沌系统也很适用于保密通信。
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