Travelling wave and optical soliton solutions of the Wick-type stochastic NLSE with conformable derivatives

In this study, we have considered Wick-type stochastic nonlinear Schrödinger equation with conformable derivatives in Kerr law media. We have constructed exact various solutions of this equation using two analytic methods, white noise analysis and Hermit transform. We have applied the inverse Hermit transform to obtain stochastic solutions and then we have shown how these stochastic solutions can be presented as Brownian motion functional solutions by two application examples.