A novel conformable fractional non-homogeneous grey model for forecasting carbon dioxide emissions of BRICS countries

Nowadays, climate change is one of the most important global issues to the international community. And nearly thirty kinds of greenhouse gases have been found in the atmosphere, of which the carbon dioxide plays a crucial role. In this paper, the carbon dioxide emissions of BRICS (Brazil, Russia, India, China and South Africa) countries are investigated by using a conformable fractional non-homogeneous grey model. The grey model is systematically studied based on the new definitions of the conformable fractional accumulation and difference. The closed-form solutions of the new model are derived by applying mathematical tools and grey theory. And the meta-heuristic algorithm ant lion optimizer is adopted to search optimal fractional order. With raw data during the period from 2000 to 2018 announced by British Petroleum, the new model is established to forecast the carbon dioxide emissions of BRICS nations from 2019 to 2025. The results show that the trend of the carbon dioxide emissions of Brazil and India is growing year by year, the pattern of Russia is fluctuant but remains stable generally, while China and South Africa reach its peak value in 2019, and then decrease in the next several years. It also demonstrates that the governments of Brazil and India should take more measures to reduce carbon dioxide emissions, while the governments of China and South Africa should keep up their crucial work on carbon dioxide emissions.