A Novel Fractional Order Grey Model with Exponential Jump and Constant Proportional Caputo–Fabrizio Derivative

Fractional calculus with a non-singular kernel has garnered significant attention in the forecasting field due to its computational simplicity and high numerical stability. To augment the capability of fractional order grey models to simultaneously capture macroscopic trends and microscopic fluctuations under event shocks, a novel fractional order grey model with exponential jump and constant proportional Caputo–Fabrizio derivative (EJCPCFGM(σ,1)), which possesses a non-singular kernel, is proposed. For this model, an operator satisfying the new information priority principle is constructed, and multiple exponentially decaying jump terms are embedded. Furthermore, a dimensionally adaptive differential evolution algorithm is utilised to optimise parameters for adaptively identifying the timing of multi-stage external shocks. When applied to forecasting electricity supply and demand in Jiangsu and Anhui provinces, experimental results confirm that the EJCPCFGM(σ,1) model substantially outperforms seven benchmark models, achieving high predictive accuracy and precisely identifying structural breakpoints. This demonstrates the model’s promising potential in forecasting complex evolutionary trends, thereby providing a scientific basis for mitigating systemic risks and facilitating cross-regional energy complementarity.