  We consider a semi-discrete finite volume scheme for a degenerate fractional
conservation laws driven by a cylindrical Wiener process. Making use of the
bounded variation (BV) estimates, Young measure theory, and a clever adaptation
of classical Kruzkov theory, we provide estimates on the rate of convergence
for approximate solutions to fractional problems. The main difficulty stems
from the degenerate fractional operator, and requires a significant departure
from the existing strategy to establish Kato's type of inequality. Finally, as
an application of this theory, we demonstrate numerical convergence rates.
