Analytical solutions of fractional modified KDV–Zakharov–Kuznetsov model utilized in fluid ions

The fractional mKDV–Zakharov–Kuznetsov (FmKDV-ZK) equation with M-truncated derivatives (MTDs) is considered. To obtain a novel rational, trigonometric, hyperbolic, and elliptic, solutions for FmKDV-ZK, we use two different methods including the modified mapping technique and generalized Riccati equation method. These methods are effective and simple. Also, they give us different kinds of solutions such as elliptic, trigonometric, hyperbolic, and rational solutions. The FmKDV-ZK equation is widely used in engineering, geophysics, meteorology, ocean dynamics, and plasma physics, therefore the obtained solutions may be applied to a wide range of important physical phenomena. Moreover, we display a wide range of solutions in two-dimensional and three-dimensional spaces to examine the effects of the MTDs operator. We conclude that the surface expands as the derivative order decreases.