Existence, Stability, and Numerical Analysis of a Caputo Fractional Population Model

Abstract

Fractional-order population models have attracted considerable attention due to their capability to describe memory-dependent biological processes more effectively than classical integer-order systems. Motivated by the limitations of traditional population growth equations in capturing hereditary effects, this paper investigates a fractional logistic population model formulated in the Caputo sense. The proposed model incorporates nonlocal memory characteristics, which play an important role in realistic biological and ecological systems. Analytical properties of the model are studied by establishing existence and uniqueness results through fixed point theory. In addition, equilibrium analysis and asymptotic stability conditions are derived for the fractional-order system. The study further demonstrates how the fractional parameter influences the growth dynamics and convergence behavior of the population. Numerical simulations and graphical illustrations are presented to validate the theoretical findings and to compare the fractional and classical models. The obtained results indicate that the Caputo fractional framework provides a more flexible and generalized approach for modeling population evolution with memory effects. The proposed methodology may also be extended to epidemic systems, predator-prey interactions, and other nonlinear biological models governed by hereditary phenomena.