<p>The increasing human population is primarily responsible for greenhouse gas emissions, with carbon dioxide being the most major and destructive. To address economic and environmental difficulties, mathematical modeling is increasingly being utilized to turn real-world problems into mathematical equations for simulations, hence improving solution understanding. This study provides a more realistic view of environmental and socioeconomic dynamics by assessing carbon dioxide emissions with a fractal-fractional mathematical model that includes memory effects and genetic characteristics. Fixed point theorems are used to prove the existence and uniqueness of the model’s solution, confirming that the system is well-posed. The Lyapunov function is also employed in global stability analysis, which provides insight into the system’s long-term behavior. To deal with chaotic events, a linear feedback control technique is used that governs system dynamics around equilibrium points. The study graphically models outcomes using numerical approaches based on Newton’s polynomial interpolation method. In order to comprehend the behavior of the system, variations in parameter values to various fractal and fractional orders are investigated while maintaining the stability of the model. The numerical results show that the long-term memory effect, represented by the fractional order derivative, has no effect on steady point stability; nonetheless, solutions tend to approach equilibrium faster while increasing fractional-order. The study emphasizes the role of memory effects on emissions reduction, economic shifts, and environmental recovery, demonstrating the importance of fractional-order mathematical modeling in environmental sustainability and making policy recommendations to minimize carbon dioxide emissions.</p>