Abstract: The issue of population aging is related to the sustainable development of the future economy and society. It is necessary to conduct an in-depth analysis and prediction of the development trend of population aging. In this study, according to the small samples and non-equidistant characteristics of the data from the first to the seventh national censuses in Inner Mongolia, the fractional order non-equidistant GM(1,1) model with optimized background value (abbreviated as OBFNEGM(1,1) model) for the total population and the aging population in Inner Mongolia are established, and the system parameters of the OBFNEGM(1,1) model are calculated by using the whale optimization algorithm. The fitting results show that the mean absolution percentage error of the proposed model is lower than that of the classical non-equidistant GM(1,1) model. On this basis, in the future eighth national census, the total population, the aging population, and the proportion of the aging population in the total population are predicted, and the suggestions to deal with the aging of the population are put forward so as to adjust the corresponding policies and measures timely. 

Key words: Population Aging, Fractional Order Accumulation, Background Value, GM(1,1) Model