In this paper, we derive optical soliton solutions with highly dispersive optical solitons in fiber Bragg gratings with stochastic perturbed Fokas–Lenells model having spatio-temporal dispersion and multiplicative white noise. In this regard, we have applied two effective methods of distinct analytical mathematical methods to find explicit solutions to many physical and engineering problems, namely addendum Kudryashov’s (AK’s) method and the unified Riccati equation expansion method (UREEM). Bright soliton, Straddled solitary solutions, singular solitons, dark soliton are acquired.