A time power-based grey model with Caputo fractional derivative and its application to the prediction of renewable energy consumption

Abstract

The development of renewable energy is related to the sustainable development of social economy and environmental protection. A time power-based grey model with Caputo fractional derivative of renewable energy consumption is established in this study by introducing Caputo fractional derivative and fractional cumulative generator into the time power-based grey model. The analytical solution of this novel model is obtained using Laplace transform, and parameters of the model are optimized using grey wolf optimization algorithm. The model is then verified by using the renewable energy consumption of China, America, and Germany as examples. Results showed that fitting and testing effect of the model is better than that of other models. Finally, the proposed model is used to predict the future development trend of renewable energy consumption in these three countries.