Abstract: We introduce the GeneRAlized Fractional Time-space graph diffusion network (GRAFT), a framework combining temporal and spatial nonlocal operators on graphs to effectively capture long-range interactions across time and space. Leveraging time-fractional diffusion processes, GRAFT encompasses a system's full historical context, while the $d$-path Laplacian diffusion ensures extended spatial interactions based on shortest paths. Notably, GRAFT mitigates the over-squashing problem common in graph networks. Empirical results show its prowess on self-similar, tree-like data due to its fractal-conscious design with fractional time derivatives. We delve deeply into the mechanics of GRAFT, emphasizing its distinctive ability to encompass both time and space diffusion processes through a random walk perspective.