In this paper, we determine the application of the Fractional Elzaki Projected Differential Transform Method (FEPDTM) to develop new efficient approximate solutions of coupled nonlinear fractional KdV equations analytically and computationally. Numerical solutions are obtained, and some major characteristics demonstrate realistic reliance on fractional-order values. The basic tools, properties and approaches introduced in He’s fractional calculus are utilized to explain fractional derivatives. The consistency of FEPDTM and the reduction in computational time give FEPDTM extensive applicability. Furthermore, the calculations concerned in FEPDTM are too simple and straightforward. It is verified that FEPDTM is an influential and efficient technique to handle fractional partial differential equations. It is being observed that FEPDTM is more efficient than known analytical and computational methods.

中文翻译：

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使用 He 分数阶计算的耦合非线性分数阶 KdV 方程的数值解

在本文中，我们确定了分数 Elzaki 投影微分变换方法 (FEPDTM) 的应用，以分析和计算耦合非线性分数 KdV 方程的新的有效近似解。获得了数值解，并且一些主要特征证明了对分数阶值的实际依赖。利用何氏分数阶微积分中介绍的基本工具、性质和方法来解释分数导数。FEPDTM 的一致性和计算时间的减少使 FEPDTM 具有广泛的适用性。此外，FEPDTM 中的计算过于简单直接。经验证，FEPDTM 是一种处理分数偏微分方程的有影响力和有效的技术。