A novel fractional grey system model with non-singular exponential kernel for forecasting enrollments

The precise enrollment forecast facilitates decision-making and ensures that educational resources are distributed fairly throughout the school system. It is, however, challenging to evaluate enrollment trends in small samples due to both internal and external factors. In order to address this issue, we present EFGM(r, 1, ect), a novel fractional-order grey prediction model based on the fractional derivative (FD) and newly proposed Riemann fractional accumulated generating operator with exponential kernel (EFAGO). The hyperparameters of the new model are calculated using the whale optimization algorithm (WOA). The proposed model was validated by using data from Shanghai, Hubei, Shaanxi and Jilin, and we drew some conclusions from the experimental results. According to our findings, the performance of our model is comparable to that of the benchmark model (including machine learning models and previous grey prediction models). During a subsequent test, the newly built model was used to predict changes in enrollment, and the results indicated that it was accurate in predicting enrollment changes. In conclusion, the authors offer some suggestions to assist decision-makers in ensuring that the educational system grows in a balanced and sustainable way over the next five years.