In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.

中文翻译：

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时间分数阶Logistic增长模型的新型两阶段分数Runge-Kutta方法

在本文中，对分数欧拉方法进行了研究，并提出了新颖的两阶段分数Runge-Kutta（FRK）方法。已经实施了所提出的分数数值方法来找到分数微分方程的解。提出的新方法将有助于导出分数阶Runge-Kutta方法的高阶族。求解了非线性分数逻辑增长模型。实例的数值结果和图表证明了该方法的有效性。