  A hybridized discontinuous Galerkin method is proposed for solving 2D
fractional convection-diffusion equations containing derivatives of fractional
order in space on a finite domain. The Riemann-Liouville derivative is used for
the spatial derivative. Combining the characteristic method and the hybridized
discontinuous Galerkin method, the symmetric variational formulation is
constructed. The stability of the presented scheme is proved. Theoretically,
the order of $\mathcal{O}(h^{k+1/2}+\Delta t)$ is established for the
corresponding models and numerically the better convergence rates are detected
by carefully choosing the numerical fluxes. Extensive numerical experiments are
performed to illustrate the performance of the proposed schemes. The first
numerical example is to display the convergence orders, while the second one
justifies the benefits of the schemes. Both are tested with triangular meshes.
