Optical random soliton solutions to conformable fractional NLSE via statistical distributions

We construct some new stochastic solutions for the fractional nonlinear Schrodinger type equation. Specifically, we introduce these stochastic solutions via geometric and beta distributions. Through these two statistical distributions, the expectation corresponding to solutions are illustrated to depict the influence of random parameters. Actually, the presented results can be used to explain many interesting phenomena in superfluid, optical fibers, plasma physics and vibration propagation in the ground and in structures. Some graphs are offered to illustrate the wave modes of the expectation corresponding to stochastic solutions. Finally, our analysis can be implemented for many other models in real life.