A novel conformable fractional-order accumulation grey model and its applications in forecasting energy consumption of China

Accurate forecasting of energy consumption demand is crucial to optimize resources and achieve sustainable development goals. However, the energy system is affected by many factors, which are complex and highly uncertain. Therefore, a novel grey model (IBCFGMP (1,1,N)) is proposed, integrating multiple optimization techniques such as background value optimization, initial condition optimization, fractional-order accumulation optimization, and grey action quantity optimization. First, this paper deduces the time response function of the optimization model. The relevant parameters of the model can be found using the particle swarm optimization algorithm. Then, the properties of the model are studied, and it is found that the optimized model have stronger universality and stability. Finally, the model is applied to predict and analyze the energy consumption of China. The prediction results indicate that China's consumption of hydroelectricity, nuclear energy, and coal will be 12.693 exajoules, 5.550 exajoules, and 98.850 exajoules in 2026, respectively. The research results will provide a scientific basis for rationally optimizing resource allocation and realizing the sustainable development of clean energy.