Analytical solution of time‐fractional Navier–Stokes equation in polar coordinate by homotopy perturbation method

Abstract

AbstractIn this letter, we implement a relatively new analytical technique, the homotopy perturbation method (HPM), for solving linear partial differential equations of fractional order arising in fluid mechanics. The fractional derivatives are described in Caputo derivatives.This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of HPM.He's HPM, which does not need small parameter is implemented for solving the differential equations. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants that can be determined by imposing the boundary and initial conditions. It is predicted that HPM can be found widely applicable in engineering. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010