Stochastic degenerate fractional conservation laws

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