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In the present work, we find the series solution for the system of fractional differential equations describing the atmospheric dynamics of carbon dioxide (CO 2) 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 CO 2 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. [ABSTRACT FROM AUTHOR]