Real-world phenomena often are modelled by the nonlinear fractional differential equations. In this work, a novel technique called the exp(-phi(epsilon)) method is employed to find the exact solutions of nonlinear FDEs. Some well-known time-fractional differential equations in the context of conformable derivative, viz. the time-fractional modified Benjamin-Bona-Mahony (BBM) equation and the time-fractional Cahn-Hilliard (CH) equation are considered to test the usefulness of the method. The utility of the expd (-phi(epsilon)) method in solving nonlinear FDEs is proved.