Abstract: The limitation of the traditional grey prediction model in handling the derivative order value may lead to unstable or even abnormal prediction results, which suggests that this issue could be a significant influencing factor. In this paper, we unveil a groundbreaking approach to grey prediction by integrating fractional differentiation through a foundation rooted in fractional differential definitions and accumulation principles. The developed model not only allows for dynamic expansion and optimization of both derivative order and accumulation operator within the grey model but also effectively addresses inherent challenges in traditional models. The proposed model exhibits an average minimum MRPE of 2.293%, representing a reduction of 1.936% compared to the average minimum MRPE achieved by the latest comparative model. The result in a more robust and adaptable prediction framework, simultaneously amplifying the model's structural variability and self-accommodating capabilities. This study provides empirical evidence that substantiates the reliability and effectiveness of our innovative prediction algorithm, thereby making a significant contribution to the advancement of the theoretical foundations of grey prediction. Finally, the paper compares the GWO and PSO optimization algorithms. The results show that GWO performs better across all indicators. Therefore, the GWO algorithm is selected to optimize the parameters of the proposed grey prediction model and is applied to three different fields. The prediction results indicate that the average annual growth rates over the next five years will be 1.26%, -1.63%, and -0.23%, respectively.