Fractional order model to study the impact of planting genetically modified trees on the regulation of atmospheric carbon dioxide with analysis and modeling

The hazard of global warming is principally caused by a rise in the atmospheric concentration of carbon dioxide (CO2). One of the main carbon dioxide sinks is forests. In this study, we examine how atmospheric carbon dioxide can be controlled as a result of genetically modified planting trees. We create a system of fractional differential equations that represents a time-fractional order model. Both qualitative and quantitative analyses are performed for the fractional order system. positiveness and boundedness of solutions of the fractional order model are verified. Fixed point theory is used to derive the uniqueness and existence of the fractional order model. Examination of Ulam-Hyers stability as well as the iterative scheme is performed by using fixed point theory. To study the effect of the fractional operator, which demonstrates the dynamical behavior of the model, solutions are generated. To demonstrate how important parameters affect the dynamics of the forest cover and atmospheric CO2 gas, numerical simulations have been created. Fractional order memory effect is examined will assist in creating conditions depending on the model's parameters.