DG-FDE: Dynamic Graph Representation Learning via Graph Neural Fractional Differential Equations

Dynamic graph representation learning learns node embeddings from evolving graphs for node property and temporal link prediction. A core challenge is that node states depend on multi-scale historical interactions, not only instantaneous graph structures. Existing continuous-time dynamic graph models rely on integer-order dynamical systems, which cannot explicitly encode long-range nonlocal history within a unified dynamics. Inspired by the nonlocal memory of fractional calculus, we propose DG-FDE, a continuous-time model that casts node representation evolution as a Caputo fractional differential equation. Its equivalent Volterra integral form uses a GNN to model time-dependent graph responses and a fractional memory kernel to aggregate historical signals. This unifies graph propagation and multi-scale temporal memory in one evolution equation. We prove finite-horizon well-posedness and derive an explicit characterization of how historical graph snapshots shape node representations. Experiments show DG-FDE outperforms its integer-order variant and strong dynamic graph baselines on standard tasks.