In this paper, we employ a sub-equation method to nd the exact solutions to the fractional (1 + 1) and (2 + 1) regularized long-wave equations which arise in several physical applications, including ion sound waves in plasma, by using a new de nition of fractional derivative called conformable fractional derivative. The presented method is more e ective, powerful, and straightforward and can be used for many other nonlinear partial fractional di erential equations.