<p>In this article, we investigate the nonlinear dynamics of the generalized fractional Kundu–Mukherjee–Naskar (gFKMN) equation, a good model for nonlinear dispersive wave behavior in some complex systems like plasma physics, fluid dynamics, nonlinear optics, and condensed matter. Through the use of fractional-order derivative, the model encodes nonlocal and memory-dependent properties that are of interest for realistic modeling of internal waves, rossby waves, and other large-scale wave patterns in the atmosphere and oceans and ultrashort pulse propagation in nonlinear optical fiber and plasma waves. The author develops a new mapping method and uses it to build a broad type of exact analytical solutions such as kink-type, singular, dark, and periodic-singular solitons. The fractional derivative order impact on the amplitude, localization, and stability of the nonlinear structures are investigated systematically. The results indicate that raising the fractional order parameter has a profound effect on wave steepening, modulation instability, and stability-unstable regimes transitions. Moreover, an in-depth modulation instability (MI) analysis is provided to elucidate the conditions for which steady-state wave trains are unstable to small perturbations, resulting in the emergence of localized structures or wave packet breakdown. This phenomenon has significant implications for understanding nonlocal wave dynamics and energy transport in earth system applications such as atmospheric blocking patterns, internal oceanic wave packets, and anomalous dispersion processes. To the best of our knowledge, this technique has not been used in current literature on this model, and an extensive fractional-order comparison has yet to be made. Additionally, this modulation instability analysis is performed here for the first time, offering novel insights into the dynamical behavior of the system.</p>