A fractional-order model for cattle–invertebrate competitive dynamics in a grassland setting

Purpose The purpose of this study is to investigate the competitive dynamics between cattle and invertebrates for grass biomass in a grassland ecosystem using a fractional-order nonlinear mathematical model. Design/methodology/approach A fractional-order grassland competition model is formulated using the Caputo fractional derivative of order ρ ∈ (0, 1]. The qualitative behavior of the system is analyzed by establishing the non-negativity and boundedness of solutions, followed by a stability analysis of the equilibrium points. Numerical simulations are performed using a generalized fractional Runge–Kutta second-order (RK2) scheme to examine the influence of fractional orders and interspecific competition parameters on system dynamics. Findings The results demonstrate that the proposed model admits biologically feasible solutions that remain non-negative and bounded. Stability analysis reveals that fractional-order dynamics significantly affect the equilibrium behavior of the system. Numerical simulations show that varying the fractional order and competition coefficients leads to substantial changes in grass biomass and population dynamics. In particular, fractional-order models exhibit enhanced stability and reduced oscillatory behavior compared to classical integer-order models. Originality/value This study provides a novel fractional-order framework for modeling grassland competition involving cattle and invertebrates. The findings highlight the advantages of fractional-order models in capturing memory effects and improving stability characteristics, offering valuable insights for ecological modeling and sustainable grassland management.