Moh. Nurul Huda, Agus Suryanto, Isnani Darti, Muhammad Fakhruddin
This study aims to analyze the dynamical model of CO2 concentration, human population, and forest biomass. Human activities and land-use changes in forested areas play an important role as the primary contributors to the increase in CO2 emissions, which drive global warming. The inclusion of fractional-order derivatives is considered to examine the long-term memory effects on the interactions within the CO2 concentration model. Theoretical results such as the existence, uniqueness, positivity, and boundedness of solutions, the local and global stability behavior of equilibrium points, and the existence of a Hopf bifurcation are explored. Furthermore, key parameters, including the deforestation rate and memory order, are investigated to determine their influence on the solution behavior of the CO2 concentration model. A fractional-order numerical scheme is employed to illustrate various scenarios, validating the theoretical findings. The results show that fractional-order changes affect the dynamic behavior of the model. In addition, increased deforestation rates can increase CO2 concentrations and reduce human population in the long term. Copyright © 2026 Published by Indonesian Biomathematical Society.
Department of Mathematics, Faculty of Sciences, Brawijaya University, Malang, 65145, Indonesia; Department of Mathematics, Faculty of Sciences, Mulawarman University, Samarinda, 75123, Indonesia; Research Center for Computing, National Research and Innovation Agency (BRIN), Bogor, 16911, Indonesia
