The fractional Rosenau–Hyman model and its approximate solution

A relatively new method called q-Homotopy Analysis Method (q-HAM) is adopted in this paper to obtain an analytical solution of the time fractional Rosenau–Hyman equation in series form. Our analysis shows the simplicity nature of the application of q-HAM to nonlinear fractional differential equations. 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 and solutions obtained by other analytical methods of the equation under various conditions. The numerical results are obtained using Mathematica 9 and MATLAB R2012b.