New Analytical Solutions for the Fractional Modified Korteweg de Vries-Zakharov-Kuznetsov Equation with Beta Derivative

This paper employs the sine-cosine method to derive new exact solutions for the modified fractional (3+1)-dimensional Korteweg-de Vries–Zakharov-Kuznetsov equation using the Beta fractional derivative approach. The effectiveness of the sine-cosine method is demonstrated through the successful construction of exact solutions, which are further illustrated with 3D and 2D graphical representations. The results highlight the potential of this method as a powerful and efficient tool for solving nonlinear fractional partial differential equations, providing insights into the behavior and structure of complex physical phenomena described by such equations.