Bitcoin has emerged as a highly attractive and reliable investment asset for financial managers, businesses, and economic firms due to its unique features such as high security, decentralization, and potential for increased income. Consequently, Bitcoin price prediction has become a significant topic of interest among financial and economic analysts and researchers. Forecasting in such contexts often involves uncertain conditions and limited information. Grey systems theory, which specializes in analyzing problems with small samples and insufficient information, offers a promising approach. This study aims to predict the price of Bitcoin using an advanced model of grey systems theory: the fractional multivariable grey model (FGM(1,N)). The FGM(1,N) model stands out by incorporating external factors into its predictions. Specifically, this research utilizes the FGM(1,3) model, considering the crude oil and gold prices to forecast Bitcoin price. The results demonstrate that the FGM(1,3) model provides more accurate predictions and better performance than the FGM(1,1) model, which does not include external factors like oil and gold prices. This study highlights the significant impact of crude oil and gold price trends on Bitcoin's market and underscores the effectiveness of the multivariable fractional grey model in financial forecasting.