Fractional approach for a mathematical model of atmospheric dynamics of CO2 gas with an efficient method

Y In the present work, we find the series solution for the system of fractional differential equations describing the atmospheric dynamics of carbon dioxide (CO2) gas using the q homotopy analysis transform method (q-HATM). The analyzed model consists of a system of three nonlinear differential equations elucidating the dynamics of human population and forest biomass in the atmosphere to the concentration of CO2 gas. In the current study, we consider Caputo-Fabrizio (CF) fractional operator and the considered scheme is graceful amalgamations of Laplace transform with q-homotopy analysis technique. To present and validate the effectiveness of the hired algorithm, we examined the considered system in terms of fractional order. The existence and uniqueness are demonstrated by using the fixed-point theory. The accomplished consequences illustrate that the considered scheme is highly methodical and very efficient in analyzing the nature of the system of arbitrary order differential equations in daily life. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

In this study, the series solution for the system of fractional differential equations describing the atmospheric dynamics of CO2 gas was found using the q homotopy analysis transform method. The model analyzed consists of three nonlinear differential equations elucidating the dynamics of human population and forest biomass in relation to CO2 gas concentration, with the use of Caputo-Fabrizio fractional operator. The results demonstrate the high methodical and efficient nature of the considered scheme in analyzing differential equations of arbitrary order in daily life.