The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy analysis transform method(q-HATM)is discussed.The projected system exemplifies three components(namely,zooplankton,toxic-phytoplankt...The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy 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.展开更多
The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the li...The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water,and the strong nonlinear effects are observed.In this paper,q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order.It offers the solution in a fast converging series.The uniqueness and convergence analysis of the considered model is presented.The given examples confirm the competency as well as accuracy of the presented scheme.The behavior of obtained solution for distinct orders of fractional derivative is dis-cussed through graphs.The auxiliary parameter¯h offers a suitable mode of handling the region of con-vergence.The outcomes reveal that the q-HATM is attractive,reliable,efficient and very effective.展开更多
文摘The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy 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.
文摘The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water,and the strong nonlinear effects are observed.In this paper,q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order.It offers the solution in a fast converging series.The uniqueness and convergence analysis of the considered model is presented.The given examples confirm the competency as well as accuracy of the presented scheme.The behavior of obtained solution for distinct orders of fractional derivative is dis-cussed through graphs.The auxiliary parameter¯h offers a suitable mode of handling the region of con-vergence.The outcomes reveal that the q-HATM is attractive,reliable,efficient and very effective.
