<p>Racism has significantly impacted the social stability of many countries worldwide. This study employs a fractional-order mathematical model to analyze the diffusion dynamics of racism and assess the influence of fractional-order derivatives and intervention strategies. We establish the boundedness and nonnegativity of model solutions, ensuring their validity. The equilibrium points of racism-free and racism-persistent states are identified, and their local stability properties are analyzed. A key finding of this study is the occurrence of a backward bifurcation, where racism persists even when the effective reproduction number is below unity. This highlights the challenges in completely eradicating racism, emphasizing the need for sustained interventions. Additionally, under specific conditions, we demonstrate that the racism-persistent equilibrium is globally asymptotically stable. To mitigate racism, we integrate optimal control strategies, incorporating antiracism measures and rehabilitation programs, and evaluate their effectiveness through numerical simulations. Our findings underscore the critical role of continuous intervention in reducing and managing racism within communities. Unlike previous studies, this work leverages the memory effect of fractional-order derivatives, capturing the long-term influence of racism and intervention strategies, and providing deeper insights into its diffusion dynamics.</p>