Explicit solution of fractional order atmosphere-soil-land plant carbon cycle system

In this paper, the dynamical behaviours and mathematics of the fractional order atmosphere-soil-land plant carbon cycle system involving the time dependent variable of carbon flux in atmosphere, the carbon flux of soil, and the carbon flux of animals and plants are qualitatively and numerically investigated. Explicit solutions in terms of the Mittag-Leffler functions to the terrestrial carbon cycle system around the equilibrium point are first time reported by applying Laplace transform of Caputo fractional derivative. The graphs of obtained solutions the time dependent variable of carbon flux in atmosphere, the carbon flux of soil and the carbon flux of animals and plants are plotted against each other. Explicit solutions to original system and stability of the fractional order linearized system around the equilibrium point are graphically compared as well.