Numerical Solution of Fractional Model for Heat Conduction in Polar Bear Hairs Equation by q-homotopy Analysis Method (q-HAM)

Abstract

In this paper, we consider the fractional model for heat conduction in polar bear hairs equation. A relatively new method called the q-homotopy analysis method (q-HAM) is adopted to obtain an analytical solution of the fractional model for heat conduction in polar bear hairs in series form. The convergence rate of the method used is faster in the sense that just very few terms of the series solution are needed for a good approximation due to the presence of the auxiliary parameter h comparable to exact solutions. Numerical solution obtained by this method is compared with the exact solution. Our error analysis shows that the analytical solution converges very rapidly to the exact solution. Numerical results are obtained using the software Mathematica.