查询词典 fractional derivative

It is important to note that the classical definition of fractional derivative in Eq.

但必须注意的是，经典的定义，分数导数在情商。

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

The exterior are belong to structure form, geometrical topology, loading case, boundary condition and other external factors. The division will be convenient for a researcher to find the real reasons affecting the dynamic characteristics of the damper. One dimensional stress and strain formulations are deduced by means of the standard derivative and fractional derivative model using the linear viscoelastic theory.

本文主要研究橡胶类粘弹性高阻尼材料及其元件的动态特性，在分析国内外关于橡胶类阻尼材料和元件的理论分析和实验研究的基础上，将影响阻尼器的因素分成属于材料特性的内在因素和属于诸如结构形式、几何尺寸、承载方式、边界条件等外在因素两大类，以利找出影响橡胶阻尼器动特性的真正原因。

We construct an explicit finite difference approximation for the equation by using the equivalence relation between Riemann-Liouville fractional derivative and Grünwald-Letnikovmake fractional derivative.

再利用Riemann-Liouville分数阶导数与Grtinwald-Letnikov分数阶导数之间的等价关系，构造一显式有限差分近似，这一离散格式可以解释为一个随机游走模型，并且收敛于稳定的概率分布。

Satisfactory numerical validation is presented including a preliminary investigation of time step effect and the value of fractional derivative order for different types of fractional differential equations.

数值算例对不同的分数阶微分方程进行了讨论，探讨了不同的分数阶和时间步长对计算结果的影响，并将计算结果与文献中相关算法的计算结果进行了比较。

In this paper,a space fractional differential equation is considered.The equation is obtained from the advection-diffusion equation by replacing the second order derivative in space by a fractional derivative in space of order.

考虑空间分数阶微分方程(即在一个标准的扩散-对流方程中，用分数阶导数代替空间二阶导数)，给出了该分数阶微分方程的显式和隐式有限差分格式。

The main research contents and results are described as follows:The constitutive equation of the elastomer modeled by the fractional derivative Maxwell model has been investigated. Based on the thermodynamics constraints analysis of the physical parameters of the fractional derivative Maxwell model, the relaxation modulus and the creeping modulus of the model are analyzed.

本论文针对该目的，采用理论研究与试验研究相结合的方法，首先研究了胶泥缓冲器的耗能机理，进而设计开发了较理想的缓冲器产品，具体研究内容和成果如下：研究了胶泥的本构模型——分数微分Maxwell模型。

We give some equivalent characterizations of Bloch type functions in term of fractional derivative, via studying the relative of growth of the different order fractional derivatives of holomorphic function, including the form of supremum and limit, the form of integral and Carleson measure, which are the generalizations of some known results in the unit disc and in the unit ball.

我们从研究全纯函数分数次导数的增长性入手，利用分数次导数给出了它的一类刻画，包括上确界和极限形式的特征，积分形式的特征以及Carleson测度形式的特征，推广了单位圆盘和单位球上一些已有的结论。

It is a non-symmetirc fractional derivative, with two-side fractional derivatives and skewness parameter,which results in the complicated disposal of the discrete form.

分数阶微分方程是指方程中含有非整数阶的导数，它非常有效地描述各种各样物质的记忆和遗传性质，在工程、物理、金融、水文等领域中发挥了越来越重要的作用。

In Chapter 3, considering fractional relaxation equation, we make use of directlythe Grunwald-Letnikov definition to discrete fractional derivative, obtain a numericalmethod of fractional relaxation equation,and give the proof of consistency ,conver-gency and stability.

第三章对于一个推广到分数阶的松驰方程，直接利用Gru¨nwald-Letnikov分数阶导数定义进行离散，得到分数阶松驰方程一个数值方法，并给出了相容性，收敛性和稳定性的证明。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。