Non-equidistance and nonhomogeneous grey model NNFGM (1, 1) with the fractional order accumulation and its application

Abstract

The most system data, used in fields of engineering technology, etc., are sequences in non-equidistance with nonhomogeneous (or approximately nonhomogeneous) characteristic. Fractional order equations can better reveal the essential properties and behaviors of objects with characteristics of fractional order. This work proposed non-equidistance fractional order accumulated generating and inverse accumulated generating operators. Based on these operators, it studied the principles and methods of establishing non-equidistance and nonhomogeneous grey model NNFGM (1,1) with the fractional order accumulation. Therefore, non-equidistance and nonhomogeneous grey model NFGM(1,1) was expanded to NNFGM(1,1). Optimization model was established. Examples show that the accuracy of the proposed model is significantly higher than that of current models.