Analytical soliton solutions of time-fractional higher-order Sasa-Satsuma equations: nonlinear optics and beyond and the impact of fractional-order derivative

The Sasa-Satsuma equation is a widely used mathematical model in the fields of nonlinear optics, ultra-short optical pulse propagation, pulse compression, telecommunications, spectroscopy, optical coherence tomography, nonlinear dynamics of optical pulses, self-steeping, self-frequency shifting resulting from stimulated Raman scattering, and higher-order dispersion of light pulses. Balancing the higher order dispersion and self-steeping, we obtain closed-form optical soliton solutions, including kink, periodic soliton, compacton, bell-shaped soliton, and others using the straightforward ( G^' / G,1 / G )-expansion approach. This study carries out a thorough investigation of analytical soliton solutions to the time-fractional higher-order Sasa-Satsuma equation, aiming to widely understand these related phenomena, and explain their significance in mathematical context. The presence of fractional derivative, which introduce memory effects and long-range interactions, finding analytical solutions for this equation is particularly challenging. The novelty of the results is supported by comparing them with previous analytical results. Moreover, we study the impact of fractional-order derivative on soliton dynamics through two-dimensional graphs and provide an explanation.