Oxygen-plankton model under the effect of global warming with nonsingular fractional order

Abstract

In this work, fractional oxygen-plankton-zooplankton mathematical model with climate change effect is considered by nonsingular fractional operators, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC). The model is based on the change in oxygen production amount of phytoplankton with the impact of global warming. Global warming influences ocean surface temperature and this case dramatically affects oxygen production of phytoplankton. We analyze the model with nonsingular fractional derivatives differently from integer case of model and we compare results with integer order case, CF and ABC cases. We show that especially ABC fractional model makes the system much more sustainable compared with the integer and CF cases. Our results show that increment of global warming has been observed to be quite effective in the oxygen production rate, resulting in the oxygen depletion and plankton extinction. (C) 2019 Elsevier Ltd. All rights reserved.