Non-equidistance Fractional Order Accumulation Grey Power Model NFGPM (1, 1) and Its Application

In scientific research and practical engineering technology applications, there are a large number of research objects with nonlinear fractional order characteristics. The correct establishment of analysis and prediction model is related to the ability to reveal the laws between parameters and the accuracy of prediction. In recent years, the gray system theory has been developed in small sample and poor information engineering practice. The present paper, a non-linear fractional accumulation gray power model NFGPM (1, 1) is proposed. Based on the multiple variables of the fractional accumulation order, the initial value correction of differential equation and the background value, the non-linear fractional cumulative gray power model was constructed, which expanded the theoretical research and practical application of fractional cumulative gray model. An example verification analysis shows that the results obtained by using the fractional cumulative gray power model are in good agreement with the references, and the analysis accuracy is high, At the same time, the model has the ability to fully discover the explicit and hidden information in the data in the case of little data and poor information, which has high engineering practical value.