Abstract
In this paper, we studied the Drinfel’d–Sokolov–Wilson equation (DSWE) and Boiti Leon Pempinelli equation (BLPE) in the conformable sense. The sine–cosine method is utilized to achieve various traveling wave solutions to the suggested nonlinear systems. It is an easy approach to use and does not require sophisticated mathematical software or a knowledgeable coder. It can also be used for various linear and nonlinear fractional issues, making it pervasive. The obtained solutions in the form of solitons emerge with the necessary constraints to ensure their existence. The obtained results hold significant role in elucidating some important nonlinear problems in applied sciences and engineering.
•The DSWE and BLPE in the conformable sense are considered.•The sine–cosine method is utilized to achieve various solutions to the suggested models.•The obtained soliton solutions emerge with the necessary constraints to ensure their existence.•Physical explanations are discussed for the obtained solutions.