The present paper employs the space-time fractional nonlinear Bogoyavlenskii equation and Schrodinger equation. We perform a new method to take some new solitary wave phenomena for each equation. Those solutions can explain through hyperbolic, trigonometric and rational func-tions. The graphical design makes the dynamics of the equations noticeable. Herein, the intended approach is simplistic, conventional, and convenient in implementing many solitary wave phenom-ena of several nonlinear fractional wave equations occurring in mathematical physics and engineer-ing as well. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).