Applicability of time conformable derivative to Wick-fractional-stochastic PDEs

Fractional-stochastic quadratic-cubic nonlinear Schrödinger equation (QC-NLSE) describing propagation of solitons through optical fibers is analyzed. Hermite transforms, white noise analysis and an improved computational method are used to investigate uncertain solutions for QC-NLSE. Specifically, Hermite transformation is applied to convert fractional-stochastic differential equations by Wick-type into deterministic fractional differential equations with an integral term. Furthermore, inverse Hermite transformation is employed to obtain stochastic solutions in the white noise space. Characteristics of presented equations are shown by using some specific values of physical arguments on obtained solutions.