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A modified fractional sub-equation method is used for constructing exact travelling wave solutions of nonlinear stochastic fractional Hirota-Satsuma Coupled KdV Equations with Conformable Derivatives. The main idea of this method is to take full advantage of the fractional Riccati equation, which has many exact solutions. Abundant white noise functional solutions are obtained for the Wick-type stochastic fractional Hirota-Satsuma coupled KdV equations via Hermite transform and white noise analysis. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions. 

Hirota-Satsuma coupled KdV equations, conformable derivative, fractional calculus, Riccati equation, white noise, Hermite transform.