  First we introduce and analyze a convergent numerical method for a large
class of nonlinear nonlocal possibly degenerate convection diffusion equations.
Secondly we develop a new Kuznetsov type theory and obtain general and possibly
optimal error estimates for our numerical methods - even when the principal
derivatives have any fractional order between 1 and 2! The class of equations
we consider includes equations with nonlinear and possibly degenerate
fractional or general Levy diffusion. Special cases are conservation laws,
fractional conservation laws, certain fractional porous medium equations, and
new strongly degenerate equations.
