To further improve the fitting and forecasting accuracy of high-order grey multivariable prediction models, this paper proposes a novel non-uniform fractional-order nonlinear grey multivariable prediction model (DLFDGM). This model achieves two key innovations: Independent fractional accumulation orders are assigned to the system characteristic sequence and each influencing factor sequence, enabling the model to adaptively optimize data processing according to the distinct fluctuation patterns and memory characteristics of each driving variable; A nonlinear term in the form of an exponential function, $\beta k^{\delta}$, is introduced to capture the marginal diminishing or scale acceleration effects of driving factors on the prediction outcomes, reflecting nonlinear dynamic behaviors. The modeling mechanism, parameter estimation, and time response equations of the proposed model are thoroughly investigated, along with discussions on its degenerative properties under specific parameter settings. The model is then applied to predict the cargo throughput of ports in Jiangsu Province, yielding a fitting accuracy of 1.05% and a forecasting accuracy of 1.91%. The results demonstrate that both fitting and prediction performance of the proposed model significantly outperform those of comparative models.