Fractional growth models: Malthus and Verhulst

Resumo

This article presents fractional versions for Malthus and Verhulst equations, based on the 𝜅-Caputo fractional derivative. Regarding the Malthus model, we present the analytical solution for the 𝜅-fractional equation. For the logistic equation, we present a numerical solution for 𝜅 → 1 and compare our results with analytical solutions found in literature. Since the numerical results obtained are different from the ones already obtained analytically, we aim to raise some discussion on this matter.