In this work, we implement a relatively new analytical technique, the Exp-Function method, for solving special form of generalized nonlinear Benjamin–Bona–Mahony–Burgers equation (BBMB) which may contain high nonlinear terms.This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of Exp-Function method. It is predicted that Exp-Function method can be found widely applicable in engineering.