A new generalized conformable fractional grey forecasting model and its applications

Purpose To address the numerical discretization errors caused by singular kernels and the overfitting risks associated with generalized operators in existing fractional grey models, this paper proposes a theoretically rigorous Generalized Conformable Fractional Grey Forecasting Model, GCFGM(1.1). Design/methodology/approach The model is established based on the right-fractional rectangular formula to ensure mathematical consistency between the continuous integral and discrete accumulation. The inverse restoration is implemented via matrix inversion to eliminate recursive errors. Furthermore, a constrained particle swarm optimization (PSO) algorithm with a regularization mechanism is designed to optimize the fractional order α and accumulation order r. This strategy mathematically constrains the solution space to balance fitting accuracy with model complexity. Findings Empirical validation is conducted across three datasets representing distinct dynamic patterns: stable exponential growth (R-GDP), saturation trends (Researchers per million inhabitants (FTE)) and irregular volatility (education expenditure). Results demonstrate that GCFGM(1,1) significantly outperforms classic integer-order and fractional models. Originality/value This study bridges the gap between continuous generalized operators and discrete time series modeling. It contributes a rigorous numerical framework that resolves the singularity issue and introduces a regularization strategy to mitigate the ill-posedness problem in small-sample forecasting.