Analytical Approach to White-Noise Functional Solutions for the Wick-Type Stochastic Fractional Zhiber-Shabat Equation

Abstract

The main aim of this paper is to give analytical approach to exact solutions for the Wick-type stochastic fractional Zhiber-Shabat equation. By means of Hermite transform, white noise theory and fractional Riccati equation method, white noise functional solutions for the Wick-type stochastic fractional Zhiber -Shabat equation are derived. Exact traveling wave solutions for the variable coefficients space-time fractional Zhiber-Shabat equations are given by using the fractional Riccati equation method. The obtained results include soliton-like, periodic and rational solutions.