An Analytic Approximation for Time-Fractional BBM-Burger Equation

Abstract

This paper attempts to carry out a study on a specific type of time-fractional differential equation called Benjamin-Bona-MahonyBurger (BBM-Burger). This equation describes the mathematical model of unidirectional transmission of low-amplitude long wavesthrough frequencydependent dispersive media. To go ahead the research, optimal homotopy asymptotic method (OHAM) and its new version (NOHAM) are applied to find analytic approximations to the BBM-Burger equation using the symbolic Maple package. Moreover, convergence of the both methods are addressed. The approximate results of the proposed methods are compared with the exact solution of BBM-Burger equation. What we learn from the results of applying OHAM and NOHAM on the BBM-Burger equation, is the high satisfactory accuracy. However, NOHAM produces an approximate solution with lower computational cost, than OHAM.