ON INVESTIGATING THE CO₂ MODEL USING CROSSOVER BEHAVIOR AND MODIFIED MITTAG–LEFFLER FRACTIONAL-ORDER DERIVATIVE

This paper elaborates the benefit of fighting the atmospheric carbon dioxide (CO 2 ) level by taking four compartmentalized mathematical models. A fractional piecewise modified Atangana–Baleanu–Caputo (mABC) derivative has been considered for the aforementioned model. The existence results and uniqueness of solution is also derived with the help of fixed point approach. To find the approximate solution for the model, we use an efficient numerical approach of Lagrange interpolation method to simulate the model. Various graphical representations are also illustrated with the help of the numerical approach and their dynamics are mentioned. This study’s key features are a novel variable-order fractional model capturing memory effects and a recent numerical methodology. Based on the simulation analysis, it appears that planting leafy trees on excess lands will be an effective method of reducing atmospheric CO 2 levels.