In this paper, the conformable and M− truncated nonlinear complex generalized Zakharov dynamical system are considered. The exact solutions of the dynamical system for different two types of derivatives are derived by using the extended rational sine−cosine and sinh−cosh methods. We make a comparison between the solutions of the Zakharov system with the conformable derivative and the system with M− truncated derivative. The results are depicted in the 2D and 3D graphics. All computations and graphics are fulfilled with the help of Wolfram Mathematica 12. The methods can be successfully applied to get soliton solutions of PDEs (or PDE systems) with the different types of derivatives.