Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

This work searches the new wave solutions of the time-fractional ion sound and Langmuir waves (ISLWs) equation and the time-fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation with the conformable derivative. The $$\left( m+\frac{1}{G^\prime }\right)$$ m + 1 G ′ -expansion method is employed for these models for the first time. Getting support from symbolic software, some new solutions are presented, which will be constructive for studies in the field of nonlinear physical phenomena. New wave solutions obtained by using the $$\left( m+\frac{1}{G^\prime }\right)$$ m + 1 G ′ -expansion method have applications in engineering, physics, and other scientific fields. The regarded method may provide a framework for the exact solutions of several evolution equations in applied sciences. Moreover, the graphical illustrations are also demonstrated to observe the dynamical behaviours of the solutions, which may benefit the development of new technologies.