Dynamic effects of human-caused carbon dioxide emissions on atmospheric temperature via various variable-order fractional derivatives

The intricate relationship between human-induced carbon dioxide (CO2) emissions and the atmospheric temperature presents a multifaceted challenge with profound implications for the environment, ecosystems, and human societies. This research presents a novel fractional variable-order model that the impact of CO2 emissions from human activities using Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional derivatives. Existence and uniqueness of fractions solutions are established and numerical simulations have been carried out based on different set of parameters to study the effects of CO2 emission caused by human activities leading to global warming.