提出了一种理想数字分数微分器系数的快速算法。
A new fast algorithm for calculating the coefficients of ideal digital fractional differentiator is presented.
证明了一类非线性项受幂函数控制的次线性分数微分方程的正解存在性。
The existence of positive solution is proved for a class of sublinear fractional differential equations where the nonlinear terms subject to the power functions.
倒向随机微分方程，分数布朗运动及其应用，随机控制等。
Backward Stochastic Differential Equation (BSDE), Fractional Brownian Motion and Its Applications, Stochastic Control, etc.
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。
The analytical conditions that the fractional-order differential systems remain chaotic are obtained by analyzing the stability of the fixed points of the systems.
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。
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.
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。
Absrtact: The calculation work of solving a fractional order differential system is huge since it relating to history.
众所周知，分数次积分算子是调和分析中以偏微分方程为背景的一种重要算子。
It is well-known that fractional integral operator is one of the important operators in harmonic analysis with background of partial differential equations.
同时，它还克服了直接用分数阶微分检测边缘时，有边缘漂移的问题。
At the same time, it overcomes the shift of the edge using fractional order differentiation directly.
采用偏微分数值模型，使用热解界面预估循环迭代的方法，对存在可变残留层材料的热解过程进行了详细研究。
The paper does an in-depth research on the numerical model of pyrolysis process of the materials with volatile residual layer by using pre-evaluation iteration method.
从分数阶微分对图像细微细节的增强能力出发，对分数阶微分的机理进行分析。
Starting from the enhanced ability of fractional differential to image details, the authors analyzed the mechanism of fractional differential.
在分析分数阶微积分的基础上，提出了一种新型模糊分数阶比例积分微分控制器。
A novel fuzzy fractional order proportional integral derivative (FFPID) controller based on fractional calculus is presented.
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。
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).
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。
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.
应用推荐