<p>This study’s primary objective is to investigate the connection between carbon emissions and global warming by tracking how these emissions causes the climatic changes spread across the environment. Based on theories established from past observations that the effect rates for various factors, a mathematical model has been built to examine the varying rates of global warming in connection to the carbon emissions. A fractional-order model with mathematical solutions for continuous monitoring is then created utilizing the Caputo operator. In addition to studying the model’s endemic places, the next generation technique is employed to determine the model’s reproduction number in these endemic sites. Sensitivity analysis was developed to identify the most sensitive parameters and examine how altering these variables affects the outcomes in different situations. A qualitative and statistical analysis of a proposed model is conducted with special focus on the existence, uniqueness, positivity, and boundedness of the solutions. At endemic sites, the model’s local stability is verified using both theoretical and statistical methods. To assess the global stability of the model, the Lyapunov derivative at the endemic point is employed. In this study, the effect of the fractional operator on a generalized power law kernel for continuous global warming monitoring related to carbon emissions is investigated. For the said purpose, numerical simulations under a two-step Lagrange polynomial technique are employed. The simulations’ outcomes show how different parameters affect the variations in global warming caused by carbon emissions. The simulations aim to replicate the effects of global warming caused by both natural processes and human activities, while also exploring various strategies for promoting a healthier environment. Our findings suggest that this research will be valuable in addressing global warming through carbon emissions and in developing effective management plans.</p>