A novel fractional grey model with Brute Force strategy and its applications in forecasting CO2 emission in Brazil and China

One of the biggest problems facing the whole world today is climate change and the problems that arise accordingly. It is very important to estimate the emission values of $CO_2$ gas, which is known as the most important of the greenhouse gases causing climate change. One of the most important and reliable methods of recent years for data forecasting is grey modeling. To address this problem, a novel conformable fractional grey model, namely FEXGM(1,1), is proposed in this study. Unlike the studies in the literature, the fractional order was also used as a parameter of the model in this modeling. Thus, with the help of the optimal fraction order, the model was able to make more effective predictions. Then, estimates of the $CO_2$ emission value of two countries that are different from each other in terms of population and industry were made.The results show that the proposed model demonstrates a higher predicted accuracy and more robust performance over the other models considered for comparison. In addition, the new grey model can be used not only for the estimation of the data in this article, but also for the estimation of all data sets.