In this equation, the diffusion is a fractional order derivative of time and space.
在此方程中，弥散项和对时间的导数为分数阶导数所代替。
The stability, controllability and observability of fractional order system are investigated.
给出了分数阶系统的稳定性条件、可控性和可观性判断依据；
At the same time, it overcomes the shift of the edge using fractional order differentiation directly.
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。
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。
A novel fuzzy fractional order proportional integral derivative (FFPID) controller based on fractional calculus is presented.
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。
This paper USES fractional order hold (FROH) to replace the traditional zero-order hold (ZOH), designs a numerical control system for the fin.
论文采用分数阶保持器(FROH)代替传统的零阶保持器(ZOH)，对减摇鳍系统进行数字控制设计。
The solution of this fractional order advection-dispersion equation is fractional stable probability distribution density with four parameters.
此方程的柯西问题的格林函数解是一分数稳定分布密度函数。
We analyzed the variation of diffusion with the fractional order by applying the numerical scheme in a test case and verified the temporal and spatial correlation.
针对理想算例进行计算求解，分析了时间和空间分数阶阶数取不同值时的扩散变化规律，验证了各自所描述的时间相关性与空间相关性。
Finally, the influences of the measurement noise and the fractional order error to the stability of this algorithm are analyzed in one-dimensional case, respectively.
最后在一维情形下分析了探测噪声和光路位置调整误差对算法稳定性的影响。
The aim of this paper is to give a simulation of creep and relaxation laws of concrete with aging by using standard-linear-like body with fractional order derivatives.
本文的目的是采用含分数阶导数的类标准线性体来模拟考虑老化的混凝土的蠕变和松弛规律。
Simulation experiments indicate that when it is given an optimal fractional order, noise can be denoised maximumly, which greatly improves the quality of speech enhancement.
实验表明在选定最佳的分数阶阶数时，可使噪声得到最大限度的滤除，大大提高了语音增强效果。
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。
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。
In order to overcome the difficulty of the discretization and application of fractional order controllers (FOC), the digital realization and control characteristic of FOC are studied in this paper.
针对分数阶控制器数值计算和应用难的问题，研究了分数阶控制器的数字实现方法和控制特性。
Based on control theories of nonlinear systems, this dissertation studies the synchronization control methods and applications of integral-order and fractional-order chaotic systems.
本文基于非线性系统控制理论，研究了整数阶混沌系统和分数阶混沌系统的同步控制方法及其应用。
Finally a stability criterion is introduced for linear non time-varying fractional-order systems.
最后介绍了一种分数阶线性定常系统的稳定性判据。
Based on the stability theory of fractional-order linear system, stability of the proposed method is analysed.
基于分数阶线性系统的稳定性理论，分析了该方法的稳定性。
The reaction order of was found to be unity and that in isobutyl alcohol to be positive fractional.
结果表明反应对铈离子为一级，对异丁醇的表观反应级数为正分数。
The axial flow in a pipe of the fractional generalized second order fluid is studied.
研究了分数阶广义二阶流体的管内轴向流动问题。
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。
Comparison with the spatial processing method using fractional lower order statistics, the proposed algorithm provides more precise DOA estimates by using the ambiguity domain information of signals.
与基于分数低阶统计量的空域处理方法相比，该文提出的算法利用了信号在模糊域中的信息，提高了算法的估计精度。
It presents a blind image watermarking scheme based on fractional Fourier domain by utilizing that the order of fractional Fourier transform is freewill.
利用分数傅立叶变换级次的任意性，提出了一种基于分数傅立叶域图象水印方案。
In order to estimate and compensate fractional pel displacements, the image signal has to be interpolated.
为了估计和补偿小数像素的偏移量，必须对图像信号进行内插。
Considering the integer-order systems analysis is happened only in positive frequency domain, this paper is concerned about the extended frequency analysis method for fractional-order control systems.
鉴于整数阶控制系统主要进行正频域分析，本文论述了分数阶控制系统的扩展频域方法。
It is shown theoretically that the fractional lower order array output power is bounded when the fractional lower order is less than half of the characteristic exponent of the noise.
理论上证明了当阶数小于噪声特征指数的一半时，分数低阶阵列输出功率有界。
Fractional lower order moment (FLOM) which also is called as fractional lower order statistics (FLOS) is one forceful tool of non-Gaussian signal analysis and processing.
分数低阶矩(FLOM)或分数低阶统计量(FLOS)是另一种非高斯信号分析处理的有力工具。
The relation between the system parameters and the order of fractional Fourier transform implemented were derived.
推导了系统结构参数与分数傅里叶变换的级次的关系。
Then, based on the multipath model, this thesis analysed and researched the time delay algorithm based on the weigthed fractional lower order covariance and the weigthed non-linear transformation.
其次，在多径时延的模型基础上，本文分析研究了加权分数低阶协方差时延估计方法和基于加权非线性变换的时延估计方法。
This dissertation has researched on the synchronization control of chaotic system and the fractional-order chaotic system and its application in secure communication.
本文研究了整数阶混沌系统和分数阶混沌系统的同步控制以及它们在保密通信中的应用。
The use of fractional-gradient operators yields more reliable results than when integer order gradients are employed.
分数阶梯度算子的使用比采用整数阶梯度产生更可靠的结果。
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