On the dynamics of a nutrient-plankton system with Caputo and Caputo-Fabrizio fractional operators

This study aims to investigate the dynamics of a nutrient-plankton system by incorporating Caputo and Caputo-Fabrizio fractional operators. We examine the impact of fractional order on the stability of the nutrient-plankton interaction. The properties of the system's solutions, such as the existence, uniqueness, and non-negativity under both operators, have been discussed. The system's equilibria has been identified, and the conditions for their stability has been analyzed. The response of the system to fractional order through numerical simulations is visualized. It is observed that the system's dynamics with the Caputo-Fabrizio fractional derivative are more similar to the system's dynamics with integer order than with the Caputo fractional derivative.