In this work, new exact solutions for nonlinear fractional DR equation and fractional approximate long water wave equation are obtained within the modified Riemann-Liouville derivative. These solutions can be useful to explain some physical phenomena. We use the (G'/G)-expansion method to establish the exact solutions for above mentioned equations. We report that this method is efficient and it is applicable to other fractional differential equations. (C) 2016 Elsevier GmbH. All rights reserved.