Numerical and Theoretical Simulation for the Carbon Absorption-Emission Model in its Fractional Form Using an Efficient Numerical Technique

Several scholars have initiated comprehensive research on the peak levels of Carbon dioxide (CO 2 ) emissions and the concept of Carbon neutrality due to the significant harm caused by global warming. This paper looks at how to illustrate and describe the Caputo-Fabrizio (CF) fractional delayed system for carbon absorption and emission. This system includes a pair of fractional differential equations (FDEs). The analysis of the model’s equilibrium point and stability is given particular attention. We evaluate numerically derived fractional integral equations using one of the most effective numerical integration techniques, Simpson’s 1/3 rule. Furthermore, we introduce several principles about the convergence of the suggested numerical scheme. We can check how effective and accurate the new process is by comparing its results to those of the Runge-Kutta method of fourth-order (RK4M) and other studies. The findings indicate that the technique serves as an efficient and a straightforwardstrument for simulating solutions to these problems.