Solving the fractional BBM–Burgers equation using the homotopy analysis method

Based on the homotopy analysis method, a scheme is developed to obtain approximation solution of a fractional BBM–Burgers equation with initial condition, which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the traditional homotopy analysis method for differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional differential equations. The solutions of our model equation are calculated in the form of convergent series with easily computable components.