A fractional Malthusian growth model with variable order using an optimization approach

Abstract

The objective is to study the population's growth with a fractional differential equation. The order of the fractional derivative is a function depending on time and the goal is to determine the fractional order function that better fits the given data. The model is than tested to describe the world population growth and of some countries. All the numerical experiments were done in MATLAB, using the routines lsqcurvefit, fminunc and spline.