Fractional approach for mathematical model of phytoplankton–toxic phytoplankton–zooplankton system with Mittag-Leffler kernel.

The solution for phytoplankton–toxic phytoplankton–zooplankton system with q-homotopy analysis transform method (q-HATM) is discussed. The projected system exemplifies three components (namely, zooplankton, toxic–phytoplankton as well as phytoplankton) and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on phytoplankton. The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana–Baleanu (AB) operator. The equilibrium points and stability have been discussed with the assistance of the Routh–Hurwitz rule in this work within the frame of generalized calculus. The fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model, and we consider five different initial conditions for the projected system. Further, the physical nature of the achieved solution has been captured for fractional order, external force and diverse mass. The achieved consequences explicate that the proposed solution method is highly methodical, easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology. [ABSTRACT FROM AUTHOR]