On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations
On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations
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DOI：
10.1016/j.apnum.2018.11.003
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发表时间：
2019-03
影响因子：
2.8
通讯作者：
Z. Odibat
中科院分区：
文献类型：
--
作者：
Z. Odibat
在本研究中，将描述一个最佳同伦分析方法来处理非线性分数阶微分方程。所提出的方法提出了一个程序，以找到一个最佳的辅助线性算子和相应的最佳初始逼近，这将加速收敛的非线性微分方程的分数阶导数的级数解。然后，提出了同伦分析方法的可靠修改版本，以方便计算。数值比较将检查所提出的算法的计算效率和相关功能。该算法有望进一步用于求解分数阶微积分中的广泛的非线性问题。
In this study, an optimal homotopy analysis approach will be described to deal with nonlinear fractional differential equations. The proposed approach presents a procedure to find an optimal auxiliary linear operator and the corresponding optimal initial approximation that will accelerate the convergence of series solutions for nonlinear differential equations with fractional derivatives. Then, a reliable modified version of the homotopy analysis method is presented to facilitate the calculations. Numerical comparison will be made to examine the computational efficiency and the pertinent features of the proposed algorithm. This algorithm is expected to be further employed to solve wide classes of nonlinear problems in fractional calculus.