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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. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to examine the behavior of the nonlinear Kaup-Newell equation. By employing the modified Kudryashov method and extended tanh function method, we have successfully derived novel solitary wave and periodic solutions. These new solutions are presented in trigonometric, hyperbolic and exponential function types. The proposed two approaches are efficient, direct and fascinating. These newly discovered solutions are illustrated using two-dimensional and three-dimensional graphs, incorporating suitable parameters values. These graphs are crucial for elucidating the dynamic properties of optical fibers. [ABSTRACT FROM AUTHOR]