Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type

Abstract

We present an analytical solution of the time-fractional foam drainage equation, using a generalised homotopy analysis method q-HAM. We considered the fractional derivative in the sense of Caputo. Comparisons are made with existing methods, which shows that the generalised homotopy analysis method q-HAM yields a better solution. The present paper shows the rapid convergence of the series of solution obtained for different values of the parameter α. This makes the method effective,
convenient and reliable.