New Solitary Wave Solutions and Dynamical Behaviors of the Nonlinear Fractional Zakharov System

In this study, we explore the fractional Zakharov system using the M-truncated derivative for the first time. Some new solitary wave and periodic solutions are derived for the fractional Zakharov equations through two advanced mathematical techniques: the fractional sine–Gordon expansion method and the fractional rational sine–cosine method. The obtained solutions are new to the fractional Zakharov equations that have not been reported in the previous literature. Visual representations of the solutions are provided using 3D and 2D graphical illustrations, offering insights relevant to associated physics and engineering disciplines. Notably, the proposed methodologies are streamlined, straightforward, and effective, holding promise for addressing various fractional evolution equations.