Sequential recommender systems are designed to capture users' evolving interests over time. Existing methods typically assume a uniform time interval among consecutive user interactions and may not capture users' continuously evolving behavior in the short and long term. In reality, the actual time intervals of user interactions vary dramatically. Consequently, as the time interval between interactions increases, so does the uncertainty in user behavior. Intuitively, it is beneficial to establish a correlation between the interaction time interval and the model uncertainty to provide effective recommendations. To this end, we formulate a novel Evidential Neural Stochastic Differential Equation (E-NSDE) to seamlessly integrate NSDE and evidential learning for effective time-aware sequential recommendations. The NSDE enables the model to learn users' fine-grained time-evolving behavior by capturing continuous user representation while evidential learning quantifies both aleatoric and epistemic uncertainties considering interaction time interval to provide model confidence during prediction. Furthermore, we derive a mathematical relationship between the interaction time interval and model uncertainty to guide the learning process. Experiments on real-world data demonstrate the effectiveness of the proposed method compared to the SOTA methods.