Sequential recommendation models analyze user historical behavior sequences to capture temporal dependencies and the dynamic evolution of interests, enabling accurate predictions of future behaviors. However, there are still two critical challenges that remain unsolved: i) Inadequate temporal modeling of user intent, which fails to distinguish between global intent tendency and temporal contextual intent. ii) Noise in sequential interaction data may introduce bias into the model. To address these issues, we propose a Self-Supervised Hypergraph Sequential Recommendation Framework (S$^2$HyRec). This framework features the Global Intent Tendency module for capturing long-term preferences, the Temporal Contextual Intent module for modeling dynamic time-sensitive interests. Additionally, we develop the Sequence Dependency-Aware module that analyzes the chronological flow of interactions to uncover inherent behavioral dynamics, further enriching the comprehensive user intent representation. To mitigate noisy interactions, we employ a Cross-View Self-Supervised Learning module that enhances the model's ability to distinguish genuine preferences from noise. Extensive experiments on four benchmark datasets demonstrate the superiority of S$^2$HyRec over various state-of-the-art recommendation methods, especially achieving average improvements of 15.13\% and 14.03\% in NDCG@10 and NDCG@20, respectively, across the four datasets. The code is provided in the Appendix.