Mathematical Modeling and Optimal Control of Carbon Dioxide Emissions

‎This paper aims to demonstrate the flexibility of mathematical models in analyzing carbon dioxide emissions and account for memory effects. ‎The use of real data amplifies the importance of this study‎. ‎This research focuses on developing a mathematical model utilizing fractional-order differential equations to represent carbon dioxide emissions stemming from the energy sector. By comparing simulation results with real-world data, it is determined that the fractional model exhibits superior accuracy when contrasted with the classical model‎. ‎Additionally‎, ‎an optimal control strategy is proposed to minimize the levels of carbon dioxide, CO2, and associated implementation costs‎. ‎The fractional optimal control problem is addressed through the utilization of an iterative algorithm‎, ‎ and the effectiveness of the model is verified by presenting comparative results.