On complex fractal-fractional order mathematical modeling of CO₂ emanations from energy sector

This research work is devoted to undertake a mathematical model for emissions of carbon dioxide (CO ₂) from energy sector using the concept of fractals-fractional differential (FFD) operator. Here, it should be kept in mind that as the population is expanding, so the need of energy increasing day by day. Burning fossil fuels accounts for a sizable amount of the world’s energy production, which increases the concentration of CO ₂ in the atmosphere and causes the global warming. It’s critical to reduce CO ₂ emissions from the energy industry. Therefore, via the use of FFD operator, we investigate a mathematical model which is addressing the mentioned process. We deduce some qualitative results regarding the existence of such models in real life using mathematical analysis. The aforesaid analysis is based on some fixed points approaches. Additionally, some analysis devoted to stability is also derived for the proposed model. In addition, a numerical algorithms based on modified Euler method is constructed to simulate the results graphically.