Traditional human motion prediction methods attempt to discover the relationship between observed and future motion sequences. However, due to the dynamic complexity of human motion, existing methods cannot fully capture the interrelationships among motion sequences, and their performance remains unsatisfactory. In this work, we propose a novel Two-stage Refinement (TSR) framework for human motion prediction. It consists of two branches: (i) a traditional motion prediction branch for preliminary prediction, and (ii) an auxiliary refinement branch designed to estimate and compensate for the preliminary prediction errors. In this way, we can obtain better prediction performance than with traditional one-stage methods. To further bridge the gap between predicted results and groundtruth, we introduce a novel fractional-order differential loss function in this work. Existing methods use only integer-order differences to capture instantaneous state changes, often failing to account for the long-range temporal dependencies in human motion. By contrast, the inherent memory effect of the fractional-order differential loss function can account for long-term dependencies and enable precise tuning of high-order trajectory derivatives, thus yielding more physically realistic motion sequences with minimal error accumulation. Comparative experiments demonstrate that our proposed Fractional Optimization-based Two-stage Refinement Framework (FOTSR) outperforms most existing works on three benchmarks (including Human3.6M, CMU-Mocap, and 3DPW).