Fractional-order Quadratic Time-varying Parameters Discrete Grey Model FQDGM (1, 1) and Its Application

Several objects in scientific research and engineering applications present fractional-order time-varying characteristics. When developing mathematical models of considering fractional-order time-varying, the dynamic analysis results are often inconsistent with the actual statistical data due to inaccurate description of the analysis model. To solve this problem, the present paper proposes a discrete grey model of fractional-order quadratic time-varying parameters based on grey fractional-order characteristics and integral theory. By taking the minimum mean relative error and the minimum mean square error as the objective function, two optimization models, namely FQDGM-I and FQDGM-II, are constructed to perform parameter estimation. A comparative analysis based on examples shows that the background value reconstructed using the proposed model is more accurate. The fitting accuracy is greatly improved compared to those obtained using previous models. These results verify the effectiveness and practicability of the proposed fractional-order quadratic time-varying parameter discrete grey model.