Dynamic fractional-order ISDR rumor propagation model incorporating refutation mechanism in complex networks.

Rumor spreading has been posing a significant threat to maintain the normal social order. In this paper, we propose a ISDR rumor propagation model on scale-free networks that considers fractional-order and refutation mechanism. we acquire basic reproduction number [Formula: see text] based on the rumor equilibrium point [Formula: see text], which thoroughly characterizes the dynamics of rumor propagation. we have demonstrated that when [Formula: see text], the rumor-free equilibrium point is globally asymptotically stable; when [Formula: see text], the rumor equilibrium point is globally asymptotically stable. Numerical simulations are provided to illustrate the main theoretical results. By analyzing the existence and uniqueness of the equilibrium solution, we demonstrate the superiority of fractional-order dynamics and refutation mechanism in the rumor propagation model. Our findings are crucial for understanding the impact of network structure on the dynamics of fractional-order systems.