Perturbation-iteration approach for fractional-order logistic differential equations

Abstract In this article, we present an accurate semi-analytical solution for fractional-order logistic equations across a wider domain. We accomplish this by deriving successive approximate solutions using a modified perturbation iteration approach tailored for fractional nonlinear differential equations. This method is also effective in addressing the cubic fractional logistic model and the Allee fractional logistic model. We provide several numerical examples to demonstrate that the perturbation iteration approach not only yields accurate approximations but also performs well across a wider domain.