This paper aims to study a two-scale population growth model in a closed system by He–Laplace method together with the fractional complex transform (FCT). The two-scale derivative is described with the help of He’s fractional derivative. The FCT approach is used to convert differential equation of the two-scale fractal order in its traditional partner, which is then readily solved by He–Laplace iterative scheme. The results are computed as a series of easily computed components. The validation of the proposed methodology is illustrated by a quantitative comparison of numerical results with those obtained using other techniques. The results show that the proposed method is fast, accurate, straightforward, and computationally reasonable.

中文翻译：

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人口动力学的两尺度分形理论

本文旨在通过 He-Laplace 方法结合分数复数变换 (FCT) 研究封闭系统中的两尺度人口增长模型。借助 He 的分数导数来描述二阶导数。FCT方法用于转换其传统伙伴中的两尺度分形阶的微分方程，然后通过He-Laplace迭代方案轻松求解。结果被计算为一系列易于计算的组件。通过数值结果与使用其他技术获得的结果的定量比较来说明所提出方法的验证。结果表明，该方法快速、准确、直观、计算合理。