Using fractional order method to generalize strengthening generating operator buffer operator and weakening buffer operator

Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases.