Population Growth Model with Fractional Operator and Its Numerical Analysis

Population models have numerous applications in economics, biology, and many other aspects. The normal growth model has an analytical solution that can be solved through an ordinary differential equation, but its fractional version is difficult to tackle. In this article, we analyze the fractional population model under the Riemann-Liouville form in the finite difference perspective with time discretization. We find that the fractional model is more suitable for fitting the data, and it captures more realistic features. Moreover, the theoretical analysis shows that the algorithm is uniformly stable in some sense, and the numerical examples are presented to support the theoretical results. We also use the COVID-19 infection as an example to demonstrate one of the various interpretations of the fractional population model.