IJAM, Volume 26, No. 3 (2013)

Abstract. The aim of this paper is to give some new approximations for the exact solutions of the Wick-type stochastic generalized fractional KdV-Burgers-Kuramoto equations with time-fractional derivatives. The homotopy analysis method (HAM) is employed to obtain approximate analytical solutions for the exact solutions of fractional KdV-Burgers-Kuramoto equations with time-fractional derivatives. Moreover, by using white noise functional analysis, Hermite transform and inverse Hermite transform we will obtained new exact solutions of the Wick-type stochastic generalized fractional KdV-Burgers-Kuramoto equations with time-fractional derivatives. Finally, by the help of the mapping relation constructed between the general formal solutions of the Wick-type stochastic generalized fractional KdV-Burgers-Kuramoto equations and the solutions of the auxiliary equations various types of the Wick-type stochastic generalized fractional KdV-Burgers-Kuramoto equations are derived.