Marine system dynamical response to a changing climate in frame of power law, exponential decay, and Mittag-Leffler kernel

The increase of sea surface temperature in ocean changes the photosynthetic production rate of phytoplankton. Therefore, it is crucial to understand the relation between temperature and phytoplanktons photosynthesis to deal the extinction caused by excessive increase in temperature. It is worth observing that temperature is one of the most principal limiting factors for phytoplanktons production due to photosynthetic enzymes work at their optimum temperature levels. In this study, the fractional oxygen-phytoplankton-zooplankton model is considered by singular and nonsingular fractional operators within Caputo, Caputo-Fabrizio, and Atangana-Baleanu in Caputo sense. The rate of oxygen production is considered by a function of temperature account for the sea surface warming. At first, the temperature function is constant and then it starts to increase, after a certain time of increase, before the oxygen depletion begins, the temperature is set to a higher secure value. With this temperature function choice, detailed numerical simulations are carried out to provide details of the internal structure of the system. We observe that the species are more sustainable in Caputo model than its corresponding integer-order model.