Approximate analytical solutions of strongly nonlinear fractional BBM-Burger's equations with dissipative term

In this article, we study and implement a relatively new analytical technique called q-Homotopy Analysis Method on the strongly nonlinear fractional BBM-Burger's equations with dissipative term. We obtain analytically, approximate solutions with two different initial conditions in the form of convergent series with easily computable components. For some special cases on the coefficient of the dissipative term, comparison is made with the exact solution and the solution obtained using other existing analytical methods. Our numerical analysis shows that this method is easy to implement and accurate when applied to strongly nonlinear partial (fractional) differential equations due to the presence of the auxiliary parameter h and the fraction factor.