Kumar, PushpendraErturk, Vedat Suat2024-05-252024-05-25202402363-62032363-621110.1007/s40808-024-01962-z2-s2.0-85187174957https://doi.org/10.1007/s40808-024-01962-zhttps://hdl.handle.net/20.500.14517/1222Kumar, Pushpendra/0000-0002-7755-2837In this article, we define a nonlinear model for exploring the strategy of combating the atmospheric level of carbon dioxide (CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}) 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 CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}. 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 CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}.eninfo:eu-repo/semantics/closedAccessCarbon dioxideMathematical modelingLiouville-Caputo fractional derivativesExistence and uniquenessPredictor-corrector methodArticleQ1WOS:001179193000001