<p>This research investigates the analytical traveling wave solutions of Sasa-Satsuma equation in a new manner by involving beta, M-truncated and conformable derivatives. The extended generalized Riccati equation mapping (EGREM) method is employed to obtain exact solutions such as bright soliton, dark soliton, kink soliton, anti-kink soliton and periodic soliton solutions. A systematic dynamical analysis, including bifurcation behavior, chaotic evolution, and parameter sensitivity, discloses the roles of fractional order and medium properties in wave propagation and stability. The results show that every fractional operator produces unique memory-based physical effects with a significant influence on dispersion, pulse shaping, and nonlinear coupling. The outcomes improve the understanding of fractional nonlinear wave models and facilitate practical applications in nonlinear optics, plasma physics, and complex signal transmission systems.</p>