Properties of the GM(1, 1) with fractional order accumulation

For traditional grey model (GM(1, 1)), it is proved theoretically that the initial condition is not utilized, and the simulative value is convex and increased or is the decreased and concave when the actual sequence is nonnegative increased. These shortcomings are the results of traditional first order accumulation on grey system model. However, for the GM(1, 1) with fractional order accumulation, the initial condition is utilized, and the monotonicity and convexity of simulative value are uncertain when the actual value is nonnegative increased. The results of practical numerical examples demonstrate that the GM(1, 1) with fractional order accumulation provides very remarkable predication performance compared with the traditional GM(1, 1) model.