Solitary wave solutions for the originating waves that propagate of the fractional Wazwaz-Benjamin-Bona-Mahony system

In this article, we discuss various solitary wave solutions that are extremely important in applied mathematics. In order to construct accurate solution to nonlinear fractional PDEs, we have employed the Khater technique to nonlinear equation for 3-dimensional fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) using conformable fractional dervatives. We obtain novel sets of solutions by employing this method including both periodic kink and periodic singular kink solu-tion, singular periodic waves solution, dark solitons, bell shaped soliton solution, bell shaped sin -gular solution, bright solution and smooth periodic wave solutions. In order to comprehend the physical principles and significance of the technique, solutions have been graphically represented. The results acquired to demonstrate the efficiency of the computational technique for the WBBM equation, our findings unambiguously demonstrate that the suggested approach is a useful, potent and simple way for experimental result for various kinds of non-integer order differential equations in the engineering and applied sciences.(c) 2023 THE AUTHORS. Published by Elsevier BV 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/).