A novel fractional-order accumulation grey power model and its application

Considering the effective service life of products, this study initially defined a generalized fractional-order accumulation generation matrix covering the effective accumulation percentage. We suggested a generalized fractional-order accumulation grey power model (GFAGMP(1,1) model) using this matrix, along with its parameter estimate, error analysis, and time response function solution. We studied transformation and the link from the generalized GM(1,1) model to GFAGMP(1,1) model on the basis of integral and power function transformation and deduced three derivation forms of this model and their application range via the class ratio analysis. Finally, different forecasting models were compared with the actual sales data of Chinese refrigerators. The results of comparison demonstrated the feasibility and effectiveness of the GFAGMP(1,1) model in forecasting the home-appliance supply chain demand in China.