Fractional order oxygen-plankton system under climate change

Global climate change affects marine species including phytoplankton, which constitute the base of the marine food web, by changing the primary productivity. Global warming affects the ocean surface temperature, in turn leading to a change in the oxygen production of phytoplankton. In this work, the fractional oxygen-phytoplankton-zooplankton mathematical model is considered by the Caputo fractional operator. The production rate of photosynthesis is determined by a temperature function. The model is, therefore, based on the idea that the rate of photosynthesis changes due to the impact of global warming, while phytoplankton oxygen production increases and decreases. We analyze the model with the Caputo fractional derivative differently from the classical case of the model and we compare the results with the integer order derivative when α tends to 1. Existence and uniqueness properties of the oxygen-plankton model have been proved by means of a local Lipschitz condition. It was shown that the species are more sustainable than its corresponding classical case in the Caputo model. Our results show that the effect of global warming on the oxygen production rate has been observed to be quite severe, resulting in oxygen depletion and plankton extinction.