In this paper, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada–Kotera (SSK) and Lax’s KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, α = 1 revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values α are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated.

中文翻译：

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基于时间分数七阶 Sawada-Kotera 和 Lax 的 KdV 方程的稳健技术解

在本文中，分数约化微分变换方法（FRDTM）用于获得初始条件（ICs）下时间分数七阶Sawada-Kotera（SSK）和Lax的KdV（LKdV）方程的级数解。在这里，分数导数是在 Caputo 意义上考虑的。获得的结果与针对特定案例的其他先前技术进行对比，α = 1揭示提出的解决方案与现有解决方案一致。此外，还研究了具有越来越多的解和绝对误差项的当前结果的收敛性分析。FRDTM 解的行为以及对不同值的影响α以图形方式说明。此外，已经证明了使用 FRDTM 获得题目问题的解决方案所花费的 CPU 时间。