Fractional-Order Model for Atmospheric $CO_{2}$ Gas Dynamics and Computational Analysis
Abstract
This study proposes and analyzes a fractional-order mathematical model to explore the interactive dynamics among the human population, forest biomass, and atmospheric carbondioxide (CO2) concentrations. The underlying system is formulated through three distinct compartments: atmospheric CO2 density (X), human population (Y), and forest biomass (Z). To incorporate memory effects and non-local behaviors, the fractional derivative is defined in the Caputo sense. Crucial qualitative properties of the model, including the existence, uniqueness, and non-negativity of the solutions, are rigorously established. Furthermore, computational simulations are conducted via the Generalized Euler Method, and the corresponding trajectories are illustrated graphically to validate the theoretical findings.
Keywords
Fractional Order Atmospheric CO2 Gas Dynamics Model, Mathematical Modeling, Generalized Euler Method, Caputo Derivative
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