In scientific research and practical engineeringtechnology applications, there are a large number of researchobjects with nonlinear fractional order characteristics. Thecorrect establishment of analysis and prediction model is relatedto the ability to reveal the laws between parameters and theaccuracy of prediction. In recent years, the gray system theoryhas been developed in small sample and poor informationengineering practice. The present paper, a non-linear fractionalaccumulation gray power model NFGPM (1, 1) is proposed.Based on the multiple variables of the fractional accumulationorder, the initial value correction of differential equation andthe background value, the non-linear fractional cumulative graypower model was constructed, which expanded the theoreticalresearch and practical application of fractional cumulative graymodel. An example verification analysis shows that the resultsobtained by using the fractional cumulative gray power modelare in good agreement with the references, and the analysisaccuracy is high, At the same time, the model has the ability tofully discover the explicit and hidden information in the data inthe case of little data and poor information, which has highengineering practical value.
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