Analytical Approach to Exact Solutions for the Wick-Type Stochastic Space-Time Fractional KdV Equation

This study is devoted to giving an analytical approach to exact solutions for the Wick-type stochastic space-time fractional KdV equation. By means of Hermite transform, white noise theory, and the fractional Riccati equation method, we derive white noise functional solutions for the Wick-type stochastic space-time fractional KdV equations. Exact traveling wave solutions for the variable coefficients space-time fractional KdV equations are given by using the fractional Riccati equation method. The obtained results include soliton-like, periodic, and rational solutions.