Fractional growth models: Malthus and Verhulst (C.Q.D. - Revista Eletrônica Paulista de Matemática, 2022)
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.
Keywords: Fractional Malthus equation; Fractional logistic equation; Mittag-leffer fuction; 𝜅-Caputo fractional derivative.