Novel solitary wave solutions to the fractional new (3+1)-dimensional Mikhailov-Novikov-Wang equation

This paper addresses the new (3+1)-dimensional Mikhailov-Novikov-Wang (MNW) equation with arbitrary order derivative and presents novel exact solutions of it by implementing exp(-phi(xi))-expansion, modified Kudryashov, generalized (G '/G)-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.