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A numerical method for solution of ordinary differential equations of fractional order

机译：一类常微分方程解的数值解法分数阶

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摘要

In this paper we propose an algorithm for the numerical solution of arbitrarydifferential equations of fractional order. The algorithm is obtained by usingthe following decomposition of the differential equation into a system ofdifferential equation of integer order connected with inverse forms ofAbel-integral equations. The algorithm is used for solution of the linear andnon-linear equations.

机译：在本文中，我们提出了一种分数阶任意微分方程数值解的算法。该算法是通过将以下微分方程分解为整数阶微分方程组并与Abel积分方程的逆形式连接而获得的。该算法用于求解线性和非线性方程。

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作者
Jacek, Leszczynski; Mariusz, Ciesielski;
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年度 2002
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正文语种 {"code":"en","name":"English","id":9}
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专利

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. On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method : Open Mathematics [J] . Haci Mehmet Baskonus, Hasan Bulut Open Mathematics . 2015,第1期

机译：作者：张莹莹，王莹，王莹，王莹
3. NUMERICAL SOLUTION OF BLACK – SCHOLES PARTIAL DIFFERENTIAL EQUATION USING DIRECT SOLUTION OF SECOND - ORDER ORDINARY DIFFERENTIAL EQUATION WITH TWO - STEP HYBRID BLOCK METHOD OF ORDER SEVEN [J] . H.K. Oduwole, J.K. Odeyemi, O.O. Olaiya Science World Journal . 2019,第2期

机译：二阶常微分方程与二阶混合块法求解二阶常微分方程的肖氏偏微分方程数值解。
4. A Numerical Method for Solution of Ordinary Differential Equations of Fractional Order [C] . Jacek Leszcyzynski, Mariusz Ciesielski International Conference on Parallel Processing and Applied Mathematics . 2002

机译：分数顺序常微分方程解决的数值方法
5. High-order Multistep Asynchronous Splitting Methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations. [D] . Gudla, Pradeep Kumar. 2016

机译：多时间尺度常微分方程数值解的高阶多步异步分裂方法（MASM）。
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. On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method [O] . Baskonus Haci Mehmet, Bulut Hasan 2015

机译：用分数adams-Bashforth-moulton方法求分数常微分方程的数值解

A numerical method for solution of ordinary differential equations of fractional order

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