In this study, we examine the nonlinear dynamics of the generalized fractional Kundu–Mukherjee–Naskar (gFKMN) equation in the context of a fractional-order model that captures the inherent memory and nonlocal interactions found in real physical systems. Utilizing the strong mapping technique \(\left( \frac{1}{\varphi (\zeta )},\frac{ \varphi '(\zeta )}{\varphi (\zeta )}\right) \) , different exact analytical solutions are obtained that feature dark and bright solitons in terms of hyperbolic tangent, hyperbolic secant, and hyperbolic cosecant functions. In order to acquire a full understanding of the rich dynamics of the system, a rigorous bifurcation analysis is conducted along with a detailed investigation of chaos, multistability, Poincaré sections, and sensitivity to initial conditions. Additional nonlinear characteristics including recurrence plots, power spectra, divergence tests, return maps, Lyapunov exponents, and time-delay embedding reconstruction methods are given to verify the existence of complex and chaotic behavior under fractional-order influences. The results show how changing the fractional order has a big impact on the amplitude, localization, and stability of the resulting wave structures. Physically, the findings have direct implications for nonlinear optical fibers, plasma wave dynamics, propagation of shallow water waves, and other dispersive media in which memory-dependent nonlinearity and long-range interactions are critical. The unified framework established here not only enhances fractional-order soliton dynamics but also provides a possible reference for the design and control of high-level nonlinear systems in fluid dynamics, photonics, and plasma physics. The principal innovation of this research is in the application of extending the generalized Kundu–Mukherjee–Naskar equation into its fractional form and incorporating exact soliton solutions with bifurcation and chaotic analysis into a single framework. The outcomes shed fresh light on how memory effects and nonlocal interactions influence soliton stability and complex dynamics, directly applicable to optics, plasmas, and fluid systems.
