In this work, we have considered the Riccati–Bernoulli sub-ODE method for obtaining the exact solutions of nonlinear fractional-order differential equations. The fractional derivatives are described in Jumarie’smodified Riemann–Liouville sense. The space–time fractional modified equal width (mEW) equation and timefractional generalised Hirota–Satsuma coupled Korteweg–de Vries (KdV) equations are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations (ODEs), which were obtained from the nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.