Applicaiton of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation

Lee Chungyi

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Applicaiton of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation

机译：分数阶微积分在线性三阶（非齐次和齐次）常微分方程中的应用

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摘要

In this paper we apply factional calculus to solve the 3rd-order ordinary differential equation of the following form: (z-α )(z-b)(z-c)ρ_3+(βz~2_γz+D) ρ_2+(α(2β-3α-3) z+αγ+α(α+1) (α +b+c))ρ_1+α(α-1)β-2α-2)ρ=f.

机译：在本文中，我们应用焦点演算来求解以下形式的三阶常微分方程：（z-α）（zb）（zc）ρ_3+（βz〜2_γz+ D）ρ_2+（α（2β-3α-3） z +αγ+α（α+1）（α+ b + c））ρ_1+α（α-1）β-2α-2）ρ= f。

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来源
《Journal of Southeast University》 |1999年第2期|115-120|共6页
作者
Lee Chungyi;
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正文语种 eng
中图分类一般工业技术;自然科学总论;
关键词
fractioanl calculus; third order differential equaiton; inear;

机译：小数演算三阶微分方程;线性的;

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专利

1. Fundamental systems and solutions of nonhomogeneous equations for a pair of mixed linear ordinary differential equations [J] . M. Venkatesulu Journal of the Australian Mathematical Society . 2009,第1期

机译：一对混合线性常微分方程的非齐次方程的基本系统和解
2. Numerical approaches to fractional calculus and fractional ordinary differential equation [J] . Li C., Chen A., Ye J. Journal of Computational Physics . 2011,第9期

机译：分数演算和分数阶常微分方程的数值方法
3. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
4. Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales [C] . Berenice C. Damasceno, Luciano Barbanti International Conference on Mathematical Problems in Engineering and Aerospace Sciences . 2014

机译：普通的分数微分方程实际上是通常的整个普通微分方程上的时间尺度
5. Malliavin calculus for backward stochastic differential equations and stochastic differential equations driven by fractional Brownian motion and numerical schemes. [D] . Song, Xiaoming. 2011

机译：Malliavin演算，用于分数布朗运动和数值格式驱动的后向随机微分方程和随机微分方程。
6. The Picard-Vessiot Theory of Homogeneous Linear Ordinary Differential Equations [O] . E. R. Kolchin 1946

机译：齐次线性常微分方程的Picard-Vessiot理论
7. Solutions to Some Homogeneous Special Ordinary Differential Equation by Means of N-Fractional Calculus Operator (On Schwarzian Derivatives and Its Applications) [O] . Nishimoto Katsuyuki 2013

机译：利用N阶微积分算子求解某些齐次特殊常微分方程（关于Schwarzian导数及其应用）
8. Asymptotic Integration Algorithms for Nonhomogeneous, Nonlinear, First Order,Ordinary Differential Equations [R] . Walker, K. P., Freed, A. D. 1991

机译：非齐次非线性一阶常微分方程的渐近积分算法

Applicaiton of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation

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