在此方程中，弥散项和对时间的导数为分数阶导数所代替。
In this equation, the diffusion is a fractional order derivative of time and space.
介绍了一种对气体体积分数进行数字化测量的新方法，分析了其工作原理及刻度方程线性化方法。
A new approach to measure digitally the gas volume fraction is described, and the working principle and the linearization method of scale equation are analyzed.
利用分离变量方法导出了在混合边界条件下的非齐次分数阶扩散-波动方程的解析解。
We derive the analytic solution of the non-homogeneous fractional diffusion-wave equation under the mixed boundary conditions using the method of separation of variables.
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.
又简介根据达西定律和水均衡原理，建立了三维有限差分数值方程及其解法。
It is briefly introduced that three-dimensional finite difference numerical equation is built according to Darcy's law and water equilibrium principle.
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.
释放第二阶段动力学过程，符合分数幂函数方程。
The modified Freundlich equation was suit to the second release process.
在分数阶微积分的理论框架下，将分形动力学的机制引入到生物黏弹性本构方程的研究中。
Within the framework of the fractional calculus theory, the mechanism of fractal dynamics is introduced to the constitutive equation research of viscoelastic materials.
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.
本文讨论了解抛物型方程的分组显式(age)方法，给出了该法和几种分数步长法的实验模型的数值比较结果。
In this paper, we discuss the method of Alternating Group Explicit (AGE) for solving 2-d parabolic equation, and give out the results of AGE method comparing with several fractional step methods.
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.
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。
The solution of this fractional order advection-dispersion equation is fractional stable probability distribution density with four parameters.
建立了含有外力的分数阶非线性对流-扩散方程。
Fractional nonlinear convection-diffusion equation with external forces is given.
考虑一个含有变系数的一维分数阶渗透方程。
In this paper, an one-dimensional fractional percolation equation with variable coefficients is considered.
在波动方程有限差分数值模拟基础上，用波形记录残差平方并建立目标函数。
The objective function can be built based on the finite difference modeling for the wave equation.
对二维三温热传导方程组提出一类分数步有限差分格式。
A kind of fractional steps finite difference scheme is introduced to solve two dimensional equations of heat conduction with three temperature.
作者通过圣维南方程组的有限差分数值解并使用比例控制方式，编写出计算机程序，实现了自动上游控制灌溉渠道系统的计算机模拟。
Based on the numerical solution of Saint Venant Equations and proportional control mode, the author established a computer program for simulating automatic upstream control irrigation canal system.
多级多组分精馏过程的数学模型，通常都由物料平衡、能量平衡、相平衡和分子分数总和四个方程组来描述，即MESH方程组。
The mathematic model of multistage multi-component distillation is composed of material equation, heat equation, and equilibrium equation, namely MESH equation.
在第4章，同伦摄动的方法被成功应用到求解带有一个可动边条件的时间分数阶扩散方程并且得到了一个近似解。
In chapter 4, Homotopy perturbation method is successfully extended to solve time-fractional diffusion equation with a moving boundary condition and an approximate solution is obtained.
该类方程的差分数值计算表明，当差分步长变小时，差分解很快逼近解析解。
A finite difference numerical calculation has shown that the smaller the difference step is, the faster the difference solution approaches the analytic one.
计算结果表明，分数形变映射法可以十分有效，它是非线性复杂方程的求解特殊新方法之一。
Some Exact Travelling Wave Solutions Of The Generalized Seventieth Order KdV Equation By The Fractionary Deforming Method;
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).
计算结果表明 ，分数形变映射法可以十分有效 ，它是非线性复杂方程的求解特殊新方法之一。
Searching for explicit and exact traveling wave solutions of Boussinesq equation by means of deformation mapping method;
两组方程中Y均代表神经功能缺损评分减少百分数。
Y in both the equations represented percentage of decrease in the neurologic defect.
两组方程中Y均代表神经功能缺损评分减少百分数。
Y in both the equations represented percentage of decrease in the neurologic defect.
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