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

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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 β in the sense of Liouville-Caputo (LC) of order α is employed while taking care of its dimensional consistency. Working parameters including conformable fractional derivative order β, LC having order α, growth rate ζ, and carrying capacity Φ 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 ζ ≥ 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.