Numerical solutions for the time fractional variant Bussinesq equation by homotopy analysis method

摘要

In this article, the fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for the nonlinear fractional variant Bussinesq equations with respect to time fractional derivative. The HAM contains a certain auxiliary h parameter which provides us a simple way to adjust and control the convergence region and rate of convergence of the series solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equation.