A new forecasting behavior of fractional model of atmospheric dynamics of carbon dioxide gas

Abstract

This paper gives insight on the nonlinear mathematical model of fractional order, which defines the dynamic variation of carbon dioxide gas (CO2) concentration in the atmosphere X(t) and examines its solution by applying an efficient technique, namely the q-homotopy analysis generalized transform method (q-HAGTM). This study also highlights the effects of variations in human population N(t) and forest biomass F(t) on the dynamics of CO2 gas concentration in the atmosphere. This technique combines the q-homotopy analysis method (q-HAM) and the generalization of the Laplace transform (GLT) to provide an accurate approximation result. The results prove that the applied technique is suitable for high approximation of the atmospheric carbon dioxide gas concentration fractional model solution and simultaneously proves the efficiency of the applied method. The fluctuating behavior of carbon dioxide gas, forest biomass, and human population concentration is illustrated by the graphical representation of the fractional derivative with variation in time. The convergence and uniqueness of the obtained solutions are evaluated for the studied fractional model. The objective of this work is to assess the pattern of CO2 and its effects on the human population and ecosystem, such as global warming and biomass variation, which in turn affect the patterns of drought, floods, storms, and the spread of climatic and vector-borne diseases.