A novel grey system model with discrete Riemann-Liouville fractional derivative and its applications.

In recent years, fractional-order grey system models have shown significant advantages in time series prediction, but their core fractional-order accumulation and difference operators often rely on complex calculations, which restrict their theoretical development and practical application. To address this issue, this paper adopts the standard product-integration rectangle rule discretization of the classical Riemann-Liouville fractional integral to derive a fractional-order accumulation operator, and further constructs the Riemann-Liouville fractional grey system model (RL-FGM). By directly introducing the fractional integral theoretical framework, this model simplifies the computation process and enhances theoretical rigor. Numerical experiments show that the proposed model is simple and effective to compute. Comparisons of prediction performance on multiple typical datasets indicate that RL-FGM significantly outperforms traditional integer-order grey models and some existing fractional-order grey models in prediction accuracy, particularly showing stronger adaptability and stability in the long memory of non-stationary sequences. This study provides a theoretically sound and easy-to-implement new approach for fractional-order grey modeling and expands its potential applications in complex time series prediction.