A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF LINEAR CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION

机译：线性卡波分数阶微分方程初值问题的数值算法

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A numerical algorithm is presented to solve the initial value problem of linear Caputo fractional-order differential equations. Error analysis has been done to Taylor series algorithm, the reason has been found why the error of the algorithm is large, the condition of using Taylor series algorithm is presented. A new algorithm called exponential function algorithm is proposed based on the analysis. Nonzero initial value problem could be transformed into zero initial value problem. The obtained fractional-order differential equation is transformed into difference equation, the numerical solution can be found with closed form solution formula. The error of the numerical solution can be modified with prediction-correction algorithm.

机译：提出了一种数值算法来解决线性Caputo分数级微分方程的初始值问题。错误分析已经完成了泰勒系列算法，已经找到了原因为什么算法的误差大，呈现了使用泰勒序列算法的条件。提出了一种基于分析的指数函数算法的新算法。非零初始值问题可以转换为零初始值问题。将获得的分数级微分方程转化为差等式，可以用封闭的溶液配方发现数值溶液。可以用预测校正算法修改数值解决方案的误差。

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《ASME/IEEE international conference on mechatronic and embedded systems and applications;ASME international design engineering technical conferences and computers and information in engineering conference》|2016年|V009T07A027.1-V009T07A027.9|共9页
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Lu Bai; Dingyue Xue;
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differential equation; fractional-order; initial value problem; numerical algorithm;

机译：微分方程分数阶初始值问题;数值算法;

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专利

1. A Refinement of Quasilinearization Method for Caputo's Sense Fractional-Order Differential Equations [J] . Co?kunYakar, AliYakar Abstract and applied analysis . 2010,第3期

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2. An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space [J] . Al-Smadi Mohammed, Djeddi Nadir, Momani Shaher, Advances in Difference Equations . 2021,第a期

机译：一种吸引人的数值算法，用于求解希尔伯特空间中的非线性Caputo-Fabrizio分数abel微分方程
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. A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF LINEAR CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION [C] . Lu Bai, Dingyu Xue ASME International Design Engineering Technical Conferences . 2016

机译：线性Caputo分数级微分方程初值问题的数值算法
5. Numerical analysis of fractional-order differential equations with nonsmooth data [D] . Zhou, Zhi. 2015

机译：数据不光滑的分数阶微分方程的数值分析
6. Data for numerical solution of Caputos and Riemann–Liouvilles fractional differential equations [O] . David E. Betancur-Herrera, Nicolas Muñoz-Galeano 2020

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7. An Improved Numerical Algorithm for the Fractional Differential Equations and Its Application in the Fractional-Order Nonlinear Systems [O] . Xiang-Jun WU, Bao-Qiang LIU 2017

机译：分数微分方程的改进数值算法及其在分数级非线性系统中的应用

A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF LINEAR CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION

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