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1)  differential order
微分阶数
2)  fractional-order differential
分数阶微分
1.
Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders.
首先,利用分数阶微分器获得特定峰信号的分数阶阶微分;然后,利用估计器Ⅰ和估计器Ⅱ提取这些特征峰信号的特征参数。
2.
A fractional-order differentiation filter is designed to obtain fractional-order differential of a given signal and to simplify computation of the fractional-order differential.
设计了一种分数阶微分滤波器。
3)  fractional differential
分数阶微分
1.
Image enhancement for rock fractures based on fractional differential
基于分数阶微分的岩石裂隙图像增强
2.
The theoretical analysis shows that fractional differentials can greatly increase high frequency,reinforce medium frequency and non-linearly preserve low frequency of signals,hence they could be used for edge and texture enhancement as well as smooth area preservation.
通过理论分析得出分数阶微分可以大幅提升信号高频成分,增强信号的中频成分、非线性保留信号的甚低频,据此得出分数阶微分应用于图像增强将使图像边缘明显突出、纹理更加清晰和图像平滑区域信息得以保留的增强图像;然后由经典的分数阶微分定义出发,推导出了分数阶差分方程,构建了近似的Tiansi微分算子。
3.
In order to improve signal noise ratio(SNR) of edge extraction,and to detect edge more effectively and exactly,according to fractional order differential difference function which was deduced from classical fractional differential G-L definition,an approximate fractional order differential Tiansi module was constructed.
为了提高图像边缘提取的信噪比,更有效和准确检测图像边缘,由信号的微分特性得出分数阶微分算子较传统1阶和2阶微分算子具有更高的信噪比,然后根据经典的G-L分数阶微分定义推导出的分数阶差分方程,构建了近似的分数阶Tiansi模板。
4)  fractional derivative
分数阶微分
1.
We examine the properties and applications of the Riemann fractional integral and derivative,and give the new definitions of left-sided fractional derivative and right-sided fractional derivative.
对一类函数的积分运算进行了讨论,获得了Riemann型分数阶微积分的一些有趣结果,并给出了函数左、右分数阶微分和积分的定义,相应地给出了函数的分数阶微分和积分的性质以及分形函数的图像。
2.
In this paper,we extend the total variation model for image denoising is which based on gradient to a new model based on fractional derivative,and then making use of the characteristic that fractional derivative and convolution integral have the same discrete formula in certain situation,We propose a variational model based on convolution integral which can be computed easily.
将基于梯度的总变分图像去噪模型推广到基于分数阶微分的模型,并根据分数阶微分与卷积运算在特殊情形下具有相同的离散格式这一特点,提出了一种易于数值计算的基于卷积积分的图像去噪变分模型,实验结果表明,新模型在提高图像信噪比的同时,可以更好地保持图像的细节信息。
5)  Order of fractional differential
分数阶微分阶次
6)  numerical fractional differentiation
数值分数阶微分
补充资料:二阶线性齐次微分方程

二阶线性微分方程的一般形式为

ay"+by'+cy=f(1)

其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0,则方程(1)变为

ay"+by'+cy=0(2)

称为二阶线性齐次微分方程,而方程(1)称为二阶线性非齐次微分方程

说明:补充资料仅用于学习参考,请勿用于其它任何用途。
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