Modern social networks are especially beneficial for spreading rumors since they perform as multichannel communication platforms. The spread of false information has a detrimental impact on people, communities, and businesses. Media reports significantly affect rumor propagation by providing inhibiting factors. In this paper, we propose a new ISCRM fractional-order model to analyze the law of rumor propagation and provide appropriate control strategies. First, under fractional differential equations, the boundedness and non-negativeness of the solutions are obtained. Second, the local and global asymptotic stability of the rumor-free equilibrium and rumor-permanence equilibrium are proved. Third, employing Pontryagin's maximum principle, the conditions necessary for fractional optimum control are derived for the rumor model, and the optimal solutions are analyzed. Finally, several numerical simulations are presented to verify the accuracy of the theoretical results. For instance, while media reports can mitigate the propagation of rumors across various dynamic regions, they are unable to completely restrain rumor spread.