Soliton and other solutions of the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with conformable derivative

In this scientific research article, we consider the (2 + 1)- dimensional Date-Jimbo-Kashiwara-Miwa equation with conformable derivative (C-DJKME), a water wave model with low surface tension and long wavelengths with weakly nonlinear restoring forces and frequency dispersion. Since the solutions of C-DJKME constitute the basis and model of many physical phenomena, we see many original studies with interesting physical properties in the literature. In our research, to acquire exact and soliton solutions of the C-DJKME, the Sardar Subequation method and the new Kudryashov method are employed for the first time. We have shown that these two methods are very effective, easily applicable, and reliable in solving such nonlinear problems. Finally, the graphs of some solutions are depicted at appropriate values of parameters. The impact of the fractional parameter on the acquired solutions is also demonstrated through 2D plots.