Abstract: The errors in the traditional FAGM (1, 1) model are analyzed, and an improved FAGM(1,1) model with the Simpson formula is proposed. Firstly, the fractional FAGM (1, 1) model is developed based on the fractional order accumulating generation operator and the inverse accumulating generation operator. Secondly, employing the Simpson formula to construct the background value of the FAGM (1, 1) model to establish the SFAGM(1,1) model. Further, the genetic algorithm is used to determine the final optimal order of the SFAGM(1,1) model to improve the prediction accuracy of the model. Finally, taking China's per capita GDP as an example, the calculation results of the SFAGM(1,1) model are compared with the GM(1,1), the GM(1,1) model with Simpson formula (SGM(1,1)) and the FAGM(1,1) model, and then the GDP per capita in the "Thirteen-Five" period is predicted. The results show that the prediction accuracy of the SFAGM(1,1) is higher than GM(1,1), SGM(1,1), and FAGM(1,1) models, and the average annual growth rate of GDP per capita during Thirteenth Five-year plan is about 10.64%. The per capita GDP in 2020 will reach 83146.97 yuan,which is 2.69 times as much as that in 2010.And in ciew of 2010 per capita GDP in China, the double goal for 2020 per capita GDP will be achieved.

Key words: fractional grey models, Simpson formula, background value, genetic algorithm, Thirteenth Five-year plan