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 \({R_0}\) based on the rumor equilibrium point \({E^*}\) , which thoroughly characterizes the dynamics of rumor propagation. we have demonstrated that when \({R_0}<1\) , the rumor-free equilibrium point is globally asymptotically stable; when \({R_0}>1\) , 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.
