Climate change and plankton dynamics: A fractional-order model-based investigation

In order to better characterise marine ecological interactions, a Caputo fractional-order model incorporating memory effects is developed in this study to investigate the population dynamics of a phytoplankton-zooplankton system. By incorporating the time-dependent reactions of phytoplankton and zooplankton, including oxygen-driven variations in phytoplankton growth and zooplankton grazing behaviour under varied maritime environments, the model goes beyond traditional differential equation techniques. The boundedness, existence, and uniqueness of solutions are established analytically, and equilibrium points reflecting coexistence and extinction scenarios are then determined. Stability is examined via the Jacobian matrix, and numerical results display equilibrium endpoints together with a mesh plot of zooplankton growth. Numerical simulations illustrate how different fractional orders influence population trajectories, demonstrating the ecological relevance of memory-driven dynamics. The results highlight the importance of fractional-order modelling in improving the understanding of oxygen-linked marine interactions and strengthening predictions of long-term ecosystem stability.