Two-Scale Fractal Theory for the Population Dynamics

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.