Novel algorithms to estimate nonlinear FDEs: Applied to fractional order nutrient-phytoplankton-zooplankton system

In this paper, dynamical behavior of a mathematical model for the interaction of nutrient phytoplankton and its predator zooplankton is investigated numerically. Stability analysis of the phytoplankton-zooplankton model is studied by using the fractional Routh-Hurwitz stability conditions. We have studied the local stability of the equilibrium points. Then a new numerical algorithm, as well as its modification for solving fractional differential equations (FDEs) based on the polynomial interpolation, is proposed. The algorithms are designed to estimate linear and nonlinear FDEs and they have the capability to apply for solving fractional order systems. The convergence order and stability of the fractional higher order algorithms are proved and stability regions of the algorithms are achieved. Extensive numerical simulation results are provided and compared with the literature for illustrating the effectiveness and applicability of the presented algorithms to solve fractional differential equations. The obtained analytical results are validated by numerical simulations and the global dynamics of the model system is studied.