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Fractional derivatives, fractional differential equations, and their numerical approximation

机译：分数阶导数，分数阶微分方程及其数值逼近

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作者
Hatcher, Christopher;
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作者单位

Tennessee Technological University;

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授予单位 Tennessee Technological University;
学科
学位 M.S.
年度 2013
页码 56 p.
总页数 56
原文格式 PDF
正文语种 eng
中图分类
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入库时间 2022-08-17 11:56:39

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1. 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。
2. Numerical Approximation of Riccati Fractional Differential Equation in the Sense of Caputo-Type Fractional Derivative [J] . Xin Liu, Yukun Yao Journal of Mathematics . 2020,第4期

机译：钙型分数衍生物意识中Riccati分数微分方程的数值近似
3. Numerical Studies for Fractional Pantograph Differential Equations Based on Piecewise Fractional-Order Taylor Function Approximations [J] . Parisa Rahimkhani, Yadollah Ordokhani Iranian Journal of Science and Technology. Transaction A, Science . 2018,第4期

机译：基于分段分数阶泰勒函数逼近的分数缩放仪微分方程的数值研究
4. The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives [C] . Arman Dabiri, Laya Karimi Annual American Control Conference . 2019

机译：Riemann-Liouville导数分数阶微分方程数值解的分数切比雪夫搭配方法
5. Numerical Approximations for the Fractional Laplacian in Space-Fractional Reaction-Diffusion Equations [D] . ?Alzahrani, Saham 2020

机译：空间 - 分数反应扩散方程分数拉普拉斯的数值近似
6. Data for numerical solution of Caputos and Riemann–Liouvilles fractional differential equations [O] . David E. Betancur-Herrera, Nicolas Muñoz-Galeano 2020

机译：Caputo和Riemann-Liouville分数阶微分方程数值解的数据
7. Numerical Approximation of Riccati Fractional Differential Equation in the Sense of Caputo-Type Fractional Derivative [O] . Xin Liu, Yukun Yao 2020

机译：钙型分数衍生物意识中Riccati分数微分方程的数值近似

Fractional derivatives, fractional differential equations, and their numerical approximation

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