Abstract
This paper addresses the new [Formula: see text]-dimensional Mikhailov–Novikov–Wang (MNW) equation with arbitrary order derivative and presents novel exact solutions of it by implementing [Formula: see text]-expansion, modified Kudryashov, generalized [Formula: see text]-expansion, and modified extended tanh-function methods. This equation emphasizes significant connection between the integrability and water waves’ phenomena. Employing the conformable derivative definition, a variety of soliton (bright, dark, anti-kink) solutions of the model are obtained. Therefore, it would appear that these approaches might yield noteworthy results in producing the exact solutions to the fractional differential equations in a wide range. In addition, 2D, 3D, and contour plots of the solutions are drawn for specific values to demonstrate the physical behaviors of the solutions.
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