An Improved the Fractional - Order Accumulated Grey Model by Trigonometric series and Its Application in Tourism Industry

In order to improve the prediction accuracy of fractional- order accumulated Grey model 
(GMr (1,1)), this study using one of special class of orthogonal series called Trigonometric series to 
modify their residual error of this model. To verify the effectiveness and the contribution of the 
proposed approach, the number of tourist visits to Quang Ninh from 2011 to 2022 is used for the 
modeling to forecast the tourism demand from 2025 to 2028. Forecasted results provided that the 
proposed model will be enhanced by 1.79% prediction accuracy compared with GMr (1,1) model. 
This result is not only show the effectiveness of proposed model but also offers valuable insights 
for Quang Ninh policymakers in orientation and planning management agency so as to boost the 
development of upcoming tourism activities.