The conformable fractional grey system model

The fractional order grey models have appealed considerable interest of research in recent years due to its high effectiveness and flexibility in time series forecasting. However, the existing fractional order accumulation and difference are computationally complex, which leads to difficulties for theoretical analysis and applications. In this paper, new definitions of fractional accumulation and difference are proposed based on the definition of conformable fractional derivative, which are called the conformable fractional accumulation and difference. Then a novel conformable fractional grey model is proposed based on the conformable fractional accumulation and difference, and Brute Force method is introduced to optimize its fractional order. The feasibility and simplicity of the proposed model and the Brute Force method are shown in the numerical example. The conformable fractional grey model outperforms the existing fractional grey model and the autoregressive model in 1 to 3-step predictions with 21 benchmark data sets, and also outperforms the existing fractional grey model in predicting the natural gas consumption of 11 countries. The results indicate that the proposed conformable fractional grey model is more efficient in longer term prediction and non-smooth time series forecasting than the existing models.