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.
Wang et al. (Thu,) studied this question.
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