Fractional-Order Accumulative Generation with Discrete Convolution Transformation

A new fractional accumulation technique based on discrete sequence convolution transform was developed. The accumulation system, whose unit impulse response is the accumulation convolution sequence, was constructed; then, the order was extended to fractional orders. The fractional accumulative convolution grey forecasting model GM(r*)(1,1) was established on the sequence convolution. From the viewpoint of sequence convolution, we can better understand the mechanism of accumulative generation. Real cases were used to verify the validity and effectiveness of the fractional accumulative convolution method.