(untitled) (Contemporary Mathematics, 2025)
This study investigates exact traveling wave solutions for the time-fractional Kundu-Mukherjee-Naskar (KMN) equation, which plays a significant role in modeling nonlinear pulse propagation in optical fibers. Two powerful analytical techniquesthe Riccati Modified Extended Simple Equation Method (RMESEM) and the Generalized Projective Riccati equations Method (GPRM) are employed to derive novel soliton and periodic wave results. Consider the fractional derivative in the conformable sense to maintain analytical tractability. Using these methods, we obtain a variety of solutions, including bright solitons, dark solitons, singular solitons, and periodic waves, expressed in terms of hyperbolic, trigonometric, and rational functions. A comparative analysis reveals the strengths and limitations of each method in handling the fractional KMN equation. The results demonstrate that both approaches are effective but yield different forms of solutions, enriching the understanding of nonlinear wave dynamics in optical media. The findings may have potential applications in nonlinear optics and photonics.