The emission of \(CO_2\) is the foremost culprit for global warming and is also considered a significant greenhouse gas. Due to the human population’s tremendous growth and activities, the rate of \(CO_2\) in the atmosphere has increased. To mitigate the emission of \(CO_2\) there are artificial ways. But, naturally have a natural resource called "Forest Biomass," one of the significant sinks to absorb \(CO_2\) during photosynthesis. Considering all these factors, the main objective of the current investigation is to understand and illustrate the importance of forest biomass in the emission of \(CO_2\) . The proposed nonlinear model consists of four variables: atmospheric \(CO_2\) , human population, energy sectors, and forest biomass. We have studied the model both qualitatively and quantitatively, which will help us make future predictions. To study the model in depth, we have formed a fractional-order model to study the system’s behavior at different ranges of fractional orders. The model is termed with the Caputo fractional operator. Boundness and Lyapunov stability for non-linear and fractional order models are studied, and equilibrium points, existence and uniqueness, and numerical simulation are examined. The Adams-Bashforth-Moulton method illustrates the essence of the system’s numerical method. The numerical approach reveals that the altered model’s stability is unchanged. Also, we have examined the model by changing the parameter values to different fractional orders to understand the system’s behavior, and the changes are captured as figures.
