As a mathematical instrument, the fractional order grey system model can be employed to characterize uncertain real-world data. This paper presents new definitions for the generalized conformable fractional accumulation (GCFA) and the generalized conformable fractional difference (GCFD). For the first time, complex network theory explains the modelling mechanisms of accumulation. Then a novel generalized conformable fractional grey model (GCFGM(1,1)) is proposed based on the GCFA and GCFD, and the particle swarm optimizer (PSO) method is employed to optimize its fractional order. In this study, the proposed model is applied to the prediction of China’s overall energy consumption, natural gas consumption, and gross domestic product. Our research reveals that our proposed model achieves mean absolute percentage error (MAPE) values of less than 5% on real datasets from 9 different regions, outperforming other comparative models. These key empirical findings demonstrate the superiority of our model in accurately predicting relevant variables.
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