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<p>The system of fractional differential equations describing the atmospheric dynamics of carbon dioxide (CO<sub>2</sub>) gas is solved in series in this study by applying the fractional forward Euler’s approach and the Toufik–Atangana method. The model under analysis comprises a set of three nonlinear differential equations that explain how the dynamics of the human population and forest biomass in the atmosphere relate to the concentration of the CO<sub>2</sub> gas. The singular kernel operator Caputo and the modified ABC fractional operator are considered in the present work. In this study, the variable fractional order has also been considered. In Mathematica, we have contrasted the proposed method with ND Solve to demonstrate and verify its efficacy. The existence and uniqueness are shown using the fixed-point theory.</p>

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A novel predictive approach for the constant and variable fractional modelling of atmospheric carbon dioxide dynamics with non-singular kernels and memory effects

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Deepika Khandelwal,
  • Sumit Gupta

摘要

The system of fractional differential equations describing the atmospheric dynamics of carbon dioxide (CO2) gas is solved in series in this study by applying the fractional forward Euler’s approach and the Toufik–Atangana method. The model under analysis comprises a set of three nonlinear differential equations that explain how the dynamics of the human population and forest biomass in the atmosphere relate to the concentration of the CO2 gas. The singular kernel operator Caputo and the modified ABC fractional operator are considered in the present work. In this study, the variable fractional order has also been considered. In Mathematica, we have contrasted the proposed method with ND Solve to demonstrate and verify its efficacy. The existence and uniqueness are shown using the fixed-point theory.