In this paper, a comparative study of natural transform decomposition method and new iterative method is presented. The proposed methods are tested upon nonlinear fractional order foam drainage problem and fractional order modified regularized long-wave equation. The solutions obtained by the proposed methods have been compared with the classical solutions and the solution obtained by Adomian decomposition method. Furthermore, the efficiency and reliability of the proposed methods are shown with the help of numerical and graphical results. The fractional order derivatives are defined in Caputo’s sense whose order belongs to the closed interval [0,1]. The results reveal that the methods are quickly convergent and yield encouraging results.

中文翻译：

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分数阶泡沫排水问题的自然变换分解法与新迭代法与分数阶修正正则长波方程的对比分析

本文对自然变换分解法和新的迭代法进行了比较研究。所提出的方法在非线性分数阶泡沫排水问题和分数阶修正正则化长波方程上进行了测试。将所提方法得到的解与经典解和Adomian分解法得到的解进行了比较。此外，在数值和图形结果的帮助下，显示了所提出方法的效率和可靠性。分数阶导数在 Caputo 的意义上定义，其阶数属于闭区间 [0,1]。结果表明，这些方法很快收敛并产生了令人鼓舞的结果。