Exact solution of the Wick-type stochastic fractional coupled KdV equations

Abstract

Fractional differential equations are widely used to model many physical phenomena in science and engineering. This paper investigates the exact solutions of Wick-type stochastic fractional variable coefficients coupled KdV equations. By implementing fractional sub-equation method based on the Kudryashov technique, new families of exact travelling wave solutions are obtained. Moreover, the obtained white noise functional solutions can be expressed as exponential type. In particular, the stochastic fractional model is reduced into a deterministic fractional one by using the Hermite transform. The results reveal that the proposed technique is very effective and simple for obtaining exact solutions of stochastic fractional partial differential equations.