非线性偏分数阶微分方程的近似解

K. Gepreel, T. Nofal
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引用次数: 0

摘要

本文通过非线性薛定谔偏分数阶微分方程和电报偏分数阶微分方程,利用定域分解方法求出线性和非线性偏分数阶微分方程的近似解。分数阶导数是用卡普托意义来描述的。我们比较了当α,β→1时部分分数阶微分方程的近似解和精确解。我们还用图来比较当α,β→1时部分分数阶微分方程的近似解和精确解。该方法对于求非线性偏分数阶微分方程的近似解具有强大的实用价值。并对变分迭代法和域分解法求得的近似解进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximate Solutions for Nonlinear Partial Fractional Differential Equations
In this article, we use  the Adomain decomposition method to find the approximate solutions for the linear and nonlinear partial fractional differential equations via the nonlinear Schrodinger  partial fractional  differential equation and the telegraph partial fractional differential equation. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. Also we make the Figures to compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. This method is powerfull to find the approximate solutions for nonlinear partial fractional differential equations. Also we will compare between the approximate solutions which obtained by using the variational itearation method and the approximate solutions which obtained by Adomain decomposition methods.
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