In this article, we define a nonlinear model for exploring the strategy of combating the atmospheric level of carbon dioxide (CO \(_2\) ) considering development activities in terms of variable-order Liouville–Caputo fractional derivatives. There are two types of variable-order Liouville–Caputo fractional derivatives used to derive the proposed model. We prove the existence and uniqueness of the solution for the given model using fixed-point theory. The numerical solution is derived by using a recently proposed predictor-corrector scheme. We perform several graphical simulations to describe the outcomes of the given model. The outputs performed at various fractional-order values provide novel findings to understand how to combat atmospheric CO \(_2\) . A novel variable-order fractional model that captures memory effects in the proposed dynamics, along with a recent numerical methodology, are the key features of this study. The simulation analysis shows that the leafy tree plantation on the excess land will be efficient against atmospheric CO \(_2\) .
