LiDAR super-resolution can improve the quality of point cloud data, which is critical for improving many downstream tasks such as object detection, identification, and tracking. Traditional LiDAR super-resolution models often struggle with issues like block artifacts, staircase edges, and misleading edges. To address these challenges, a novel super-resolution model of LiDAR based on fractional-order total variation (FOTV) is proposed in this paper. We propose a FOTV regularization optimization problem, utilizing an end-to-end trainable iterative network to capture data attributes.This enables the precise reconstruction of fine details and complex structures in point clouds. Specifically, the half-quadratic splitting algorithm divides the problem into data fidelity and prior regularization subproblems. We then propose a deep unfolding network, which iteratively deals with the two subproblems within the FOTV-HQS framework. Numerous experiments have shown that our approach significantly reduces the number of parameters by up to 99.68% and maintains good performance, making it ideal for applications with limited compute and storage resources.