Effects of greenhouse gases and hypoxia on the population of aquatic species: a fractional mathematical model.

Abstract

Study of ecosystems has always been an interesting topic in the view of real-world dynamics. In this paper, we propose a fractional-order nonlinear mathematical model to describe the prelude of deteriorating quality of water cause of greenhouse gases on the population of aquatic animals. In the proposed system, we recall that greenhouse gases raise the temperature of water, and because of this reason, the dissolved oxygen level goes down, and also the rate of circulation of disintegrated oxygen by the aquatic animals rises, which causes a decrement in the density of aquatic species. We use a generalized form of the Caputo fractional derivative to describe the dynamics of the proposed problem. We also investigate equilibrium points of the given fractional-order model and discuss the asymptotic stability of the equilibria of the proposed autonomous model. We recall some important results to prove the existence of a unique solution of the model. For finding the numerical solution of the established fractional-order system, we apply a generalized predictor-corrector technique in the sense of proposed derivative and also justify the stability of the method. To express the novelty of the simulated results, we perform a number of graphs at various fractional-order cases. The given study is fully novel and useful for understanding the proposed real-world phenomena.