The proliferation of the Internet and mobile devices has made it increasingly easy to propagate rumors on social media. Widespread rumors can incite public panic and have detrimental effects on individuals. In recent years, researchers have found that both the spatial structure of rumor diffusion and the temporal features of propagation can be effective in identifying rumors. However, existing methods tend to focus on either spatial structure or temporal information in isolation, and few models can effectively capture both types of information. Additionally, most existing methods treat continuously changing temporal information as static snapshots, neglecting the precise timing of propagation. Moreover, as users repost and comment, background knowledge associated with the posts also evolves dynamically, which is often ignored. To address these limitations, we propose CGNKP (Continuous-time Dynamic Graph Networks integrated with Knowledge Propagation), a model that jointly captures the spatial structure and continuous-time features of post propagation to fully understand the dynamics of background knowledge. Specifically, we introduce a novel method for encoding continuous-time dynamic graphs, modeling the propagation process through two dynamic graphs: a temporal propagation graph (for posts diffusion) and a temporal knowledge graph (for knowledge diffusion). Extensive experiments on real-world datasets demonstrate that CGNKP significantly outperforms multiple strong baselines, achieving accuracies of 0.861 on the Twitter15 dataset and 0.903 on the Twitter16 dataset.