  In this article, we explore some of the main mathematical problems connected
to multidimensional fractional conservation laws driven by L\'evy processes.
Making use of an adapted entropy formulation, a result of existence and
uniqueness of a solution is established. Moreover, using bounded variation (BV)
estimates for vanishing viscosity approximations, we derive an explicit
continuous dependence estimate on the nonlinearities of the entropy solutions
under the assumption that L\'evy noise depends only on the solution. This
result is used to show the error estimate for the stochastic vanishing
viscosity method. Furthermore, we establish a result on vanishing non-local
regularization of scalar stochastic conservation laws.
