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In the new model, the original sequence is first transformed by using the weighted fractional-accumulation generating operator, which involves two parameters. With special choices of these parameters, the proposed WFGM(1,1) model reduces to the classical GM(1,1) model and the fractional GM(1,1) (FGM(1,1)) model, as well as the new information priority GM(1,1) (NIPGM(1,1)) model studied recently. Stability property of the WFGM(1,1) model is studied in detail. In practice, the quantum particle swarm optimization algorithm is adopted to choose the quasi-optimal parameters for the new model so as to get the best fitting accuracy. Finally, four numerical examples from different practical applications are present. 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