Recommender systems are essential for personalized content delivery and have become increasingly popular in recent years. However, traditional recommender systems are limited in their ability to capture complex relationships between users and items. Recently, dynamic graph neural networks (DGNNs) have emerged as a promising solution for improving recommender systems by incorporating temporal and sequential information in dynamic graphs. In this paper, we propose a novel method, “Ti-DC-GNN” (Time-Interval Dual Causal Graph Neural Networks), based on an intermediate representation of graph evolution as a sequence of time-interval graphs. The main parts of the method are the novel forms of interval graphs: graph of causality and graph of consequence that explicitly preserve inter-relationships between edges (user-items interactions). The local and global message passing are developed based on edge memory to identify both short-term and long-term dependencies. Experiments on several well-known datasets show that our method consistently outperforms modern temporal GNNs with node memory alone in dynamic edge prediction tasks.