water gases hypoxia Effects of greenhouse gases and hypoxia on the population of aquatic species: a fractional mathematical model simulated results unique solution solution study derivatives decrement technique https://doi.org/10.1186/s13662-022-03679-8 equilibrium method articles autonomous model important results quality oxygen point real-world phenomena view prelude problem true stability 2022-10-01T06:50 fractional mathematical model existence form equilibrium point reasons cause article model effect greenhouse gases fractional order case study of ecosystems predictor-corrector technique topic aquatic animals density phenomenon rate of circulation aquatic species 2022-04-15 temperature fractional-order model paper sense numerical solution 31 results cases novelty system number interesting topic water causes temperature of water fractional-order systems population 2022-04-15 dynamics fractional derivative ecosystems graph circulation number of graphs https://scigraph.springernature.com/explorer/license/ asymptotic stability mathematical model real-world dynamics Caputo fractional derivative 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. rate species animals levels generalized form oxygen levels Pushpendra Kumar pub.1147152169 dimensions_id Pure Mathematics Govindaraj V. 10.1186/s13662-022-03679-8 doi Erturk Vedat Suat 35450200 pubmed_id Mathematical Sciences Mohamed Mohamed S. Springer Nature - SN SciGraph project Springer Nature 2731-4235 1687-1839 Advances in Continuous and Discrete Models 2022 Department of Mathematics, National Institute of Technology Puducherry, 609609, Karaikal, India Department of Mathematics, National Institute of Technology Puducherry, 609609, Karaikal, India Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, 55200, Atakum, Samsun, Turkey Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, 55200, Atakum, Samsun, Turkey Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia 1