Short-term electrical load series forecast plays an essential role in energy demand management, however power consumption data are non-stationary, nonlinear and multi-dimensional series, leaving prediction a difficult task. Recently, fractional- order partial differential equations are attracting attention as they have been successfully utilized to describe power consumption behaviors in complex electrical systems and power grids. In this paper, a clustering fractional order predictive model called C-FGM is introduced for short-term electrical load forecast missions. The novelty of the C-FGM is that it initiates a parameter α to describe the accumulative weather trends of multiple clustering sub-series, and this parameter is also assigned to a fractional-order partial differential equation to depict the previous power series. Hyper parameters of these equations are then sent to a global optimization algorithm to reduce predictive errors. Simulation results on two electricity datasets demonstrated that our algorithm can learn from datasets hyper parameters inside equations and produce forecast values efficiently. Com- pared with contemporary models such as LSTM and the Transformer, C-FGM clearly achieved a higher accuracy (MAPE from 1.97 to 4.67%, outperforms LSTM whose average MAPE is 4.34% and Transformer whose average MAPE is 5.42%). This satisfactory performance suggests that our data-driven model can be used as an effective tool for real time forecasting missions.