Fractional order grey reducing generation operator and its properties

By utilizing Gamma function expanded for integer factorial, this paper expands one order reducing generation operator into integer order reducing generation operator and fractional order reducing generation operator, and gives the analytical expression of fractional order reducing generation operator. Actually, one order reducing generation operator and integer order reducing generation operator are both special cases of fractional order reducing generation operator. Theoretical proof and numerical simulation shows that fractional order reducing generation operator satisfies commutative law, exponential law and other properties. Expanding the reducing generation operator would help develop grey prediction model with fractional order operators and widen the application fields of the grey prediction model.