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An effective approach to solve a system fractional differential equations
Alexandria Engineering Journal ( IF 6.8 ) Pub Date : 2020-09-08 , DOI: 10.1016/j.aej.2020.08.015
H. Jafari , M.A. Firoozjaee , S.J. Johnston

The manuscript details a numerical method for solving a system of fractional differential equations (SFDEs) based on the Caputo fractional derivative by the Ritz method. To use this method, we transform the SFDEs into an optimization problem and obtain the system of nonlinear algebraic equations. Using polynomials of basis functions, we approximate solutions and obtain the coefficients of polynomial expansions by solving the system of nonlinear equations. We debate the convergence analysis of the proposed technique. Some numerical examples are included to assert the theoretical results and the performance of the numerical approximation.



中文翻译:

解决系统分数阶微分方程的有效方法

该手稿详细介绍了一种基于Caputo分数阶导数的丽思方法求解分数阶微分方程(SFDE)系统的数值方法。要使用此方法,我们将SFDE转化为一个优化问题,并获得非线性代数方程组。使用基函数的多项式,我们通过求解非线性方程组来近似解并获得多项式展开的系数。我们辩论所提出技术的收敛性分析。包括一些数值示例,以证明理论结果和数值逼近的性能。

更新日期:2020-09-29
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