An efficient hybrid computational technique for the time dependent Lane-Emden equation of arbitrary order

Abstract

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 discussed through graphs. The auxiliary parameter ħ offers a suitable mode of handling the region of convergence. The outcomes reveal that the q-HATM is attractive, reliable, efficient and very effective.

Keywords

• Fractional differential equations (FDE)
• Time dependent Lane-Emden type differential equation
• Caputo derivative of arbitrary order
• q-homotopy analysis transform scheme (q-HATM)
• Laplace transform