Periodic structures of solitons and shock wave solutions in the fractional nonlinear Shynaray-IIA equation via a generalized analytical method.

In this research, we utilized the Jacobi elliptic function expansion method to study the truncated M-fractional nonlinear Shynaray-IIA (S-IIA) equation with computational simulations. With the use of a truncated M-fractional derivative, the nonlinear (1 + 1)-dimensional Shynaray-IIA equation can be effectively solved using the Jacobi elliptic function expansion approach. This method yields new exact optical soliton wave solutions that display a range of intriguing features. In particular, we derive the solutions in terms of Jacobi elliptic functions, which are very useful for understanding complex physical events. Additionally, solitary wave and shock wave solutions emerge in the limiting instances for [Formula: see text] and [Formula: see text] respactively, offering information on periodic oscillations and localized wave behavior. To aid in understanding and enable a more thorough examination of their features, a number of these solutions are graphically depicted in several dimensions 2D, 3D and contour plots. There are numerous fields in which the Jacobi elliptic function expansion method is used, including fluid dynamics, plasma physics and quantum mechanics. This approach enhances our understanding and makes it possible to predict real-world phenomena more accurately.