Retinal vessel segmentation is essential for the diagnosis and treatment planning of retinal diseases, yet remains challenging due to weak edges, tiny branches, and complex background textures. In this paper, we propose Frac-SegNet, a deep segmentation network that integrates fractional-order modelling at the preprocessing, feature extraction, and loss levels to improve the continuity and robustness of retinal vessel extraction. First, a Grünwald–Letnikov fractional differential operator is used to generate multi-directional edge responses, which are concatenated with the original fundus image to form an augmented multi-channel input. Second, adaptive fractional-order convolution blocks are embedded into a U-Net–like encoder–decoder architecture, where learnable order weights dynamically fuse integer-order and fractional-order responses, enabling simultaneous modeling of local details and long-range dependencies. Third, a composite loss is designed by combining Dice loss, total variation (TV) regularization, and a fractional gradient constraint that enforces consistency between the fractional-order gradients of the prediction and the ground truth. Experiments on the DRIVE, STARE, and CHASE DB1 datasets demonstrated that FracSegNet achieved competitive or superior performance compared with state-of-the-art methods, with F1 scores above 0.83 and clear improvements in edge continuity and fine-branch preservation. These results indicate that fractional-order modeling provides an effective and generalizable paradigm for segmenting weak edges and delicate vascular structures in medical images.