Analytical Solution for the Time Fractional BBM-Burger Equation by Using Modified Residual Power Series Method

In this study, a generalized Taylor series formula together with residual error function, which is named the residual power series method (RPSM), is used for finding the series solution of the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The BBM-Burger equation is useful in describing approximately the unidirectional propagation of long waves in certain nonlinear dispersive systems. The numerical solution of the BBM-Burger equation is calculated by Maple. The numerical results show that the RPSM is reliable and powerful in solving the numerical solutions of the BBM-Burger equation compared with the exact solutions as well as the solutions obtained by homotopy analysis transform method through different graphical representations and tables.