Fractional modelling for BBM-Burger equation by using new homotopy analysis transform method

Abstract

The purpose of this study is to introduce a new analytical method namely, fractional homotopy analysis transform method (FHATM) for series solution of the time fractional BBMBurger equation. The homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm (LTA) for nonlinear fractional partial differential equation in fluid dynamics and makes the calculation much simpler. The proposed scheme finds the solutions of nonlinear problems without any discretization, restrictive assumptions and avoids the rounding off errors. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.