This research explored optical soliton solutions for the (2+1)-dimensional generalized fractional Kundu-Mukherjee-Naskar equation (gFKMNE), which is a nonlinear model for explaining pulse transmission in communication structures and optical fibers. Two enhanced variants of $(\frac{G^{\prime }}{G})$-expansion method were employed, namely, extended $(\frac{G^{\prime }}{G})$-expansion method and the generalized $(r+\frac{G^{\prime }}{G})$-expansion method, based on the wave transformation of the model into integer-order nonlinear ordinary differential equations (NODEs). By assuming a series-form solution for the resultant NODEs, these strategic methods further translated them into a system of nonlinear algebraic equations. Solving these equations provided optical soliton solutions for gFKMNE using the Maple-13 tool. Through 3D and contour visuals, it was revealed that the constructed soliton solutions are periodically arranged in the optical medium, forming dark soliton lattices. These dark soliton lattices are significant in several domains, such as optical signal processing, optical communications, and nonlinear optics.

In this paper, a class of nonlinear impulsive pantograph-type Hilfer complex-valued systems (IPH-CVSes) is investigated. Two cases corresponding to the fractional orders $\rho \in (0,1)$ and $\rho \in (1,2)$ are studied. Explicit solution representations for the considered models are derived. Moreover, existence and uniqueness results are established using Krasnoselskii's fixed-point theorem and the Banach contraction principle. Finally, an application arising from an aerodynamic flow model is provided to demonstrate the applicability of the obtained theoretical results.

The Riccati-Bernoulli sub-ODE method has been used in recent research to efficiently investigate the analytical solutions of a non-linear equation widely used in fluid dynamics research. By utilizing this method, exact solutions are obtained for the space-time fractional symmetric regularized long-wave equation. These results comprehensively understand the long wave equation widely used in numerous fluid dynamics and wave propagation scenarios. The approach to studying these phenomena and using conceptual representation to understand their essential characteristics opens the door to valuable insights that may help improve both the theoretical and applied aspects of fluid dynamics and similar fields. Thus, as these complex equations demonstrate, the suggested approach is a valuable tool for conducting further research into non-linear phenomena across several disciplines.