Abstract
This work investigates the Wick-type stochastic and extended Korteweg-de Vries (EKdV) equation under conformable differential operators. Novel wave solutions with soliton and periodic types are produced to the deterministic EKdV under conformable differential operators. Abundant stochastic wave solutions are explored for the Wick-type stochastic EKdV equation by using conformable differential operators and the inverse Hermite transform. The stochastic soliton and periodic solutions are denoted as functional solutions with Brownian motion environment. For the acquired solutions, comparisons and graphical representations with three-dimensional graphs are shown for peculiar values of the existing parameters. According to the existing literature, utilization of the conformable differential operators is a novel contribution for solving the stochastic EKDV and other stochastic nonlinear problems.