  We consider the Cauchy problem for a degenerate fractional conservation laws
driven by a noise. In particular, making use of an adapted kinetic formulation,
a result of existence and uniqueness of solution is established. Moreover, a
unified framework is also established to develop the continuous dependence
theory. More precisely, we demonstrate L^1-continuous dependence estimates on
the initial data, the order of fractional Laplacian, the diffusion matrix, the
flux function, and the multiplicative noise function present in the equation.
