Fractional numerical dynamics for the logistic population growth model under Conformable Caputo: a case study with real observations

Models of population dynamics are substantially non-Markovian in nature and exhibit behavior for memory effects. This research study investigates the logistic growth model from population dynamics under both classical and non-classical (fractional) differential operators using actual statistical data. For the non-classical differential operator, the operator called conformable fractional derivative having order beta in the sense of Liouville-Caputo (LC) of order alpha is employed while taking care of its dimensional consistency. Working parameters including conformable fractional derivative order beta, LC having order alpha, growth rate zeta, and carrying capacity phi have been optimized, and the results are compared with those of classical one. Error rate suggests the superiority of the fractional conformable logistic model whose solutions are investigated for uniqueness via fixed point theory. Numerical simulations using Adams' iterative technique recently proposed for the conformable fractional derivative are illustrated in figures for a thorough understanding of the model's behavior, along with a statistical summary for the operators. An attractive chaotic attractor is observed in the fractional logistic model when zeta >= 4.023. Cumulative effects of growth rate and carrying capacity on the population's change in the logistic model are also investigated with 3D graphics.

Automated summary

The study investigates the logistic growth model in population dynamics using both classical and non-classical differential operators with actual statistical data. The results suggest the superiority of the fractional conformable logistic model, which is explored for uniqueness through fixed point theory. Numerical simulations using the Adams iterative technique illustrate the model's behavior and provide a statistical summary of the operators.