Derivative (finance)

Physics

Sociology

Population

Mathematics

Fractal

Biology

Laplace transform

Financial economics

Algorithm

Mathematical optimization

Demography

Fractional calculus

Mathematical analysis

Series (stratigraphy)

Paleontology

Economics

Scale (ratio)

Computer science

Quantum mechanics

Applied mathematics

Fractals

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.

TWO-SCALE FRACTAL THEORY FOR THE POPULATION DYNAMICS