Application of the sardar sub equation method to the fractional M-derivative differential equation

In this study, the exact solutions of the variant Boussinesq system, expressed by a nonlinear partial differential equation to model the behavior of shallow water waves, have been obtained. This system of equations is a modification of the original Boussinesq system. The traveling wave solutions of the fractional M-derivative variant Boussinesq system were obtained using the Sardar sub-equation method. To solve this system of equations, the wave transformation was applied to the partial differential equation, reducing it to an ordinary differential equation. The purpose of this thesis is to shed ligh on the mathematical structures represented by the fractional M-derivative model and to contribute to a better understanding of the system 2D, 3D and contour graphs were obtained. As a result, it has been stated that the Sardar sub-equation method for such systems of equations. Furthermore, it can be suggested that this method is applicable to diffrnt fractional models as well.