  In this paper, the boundary element method is combined with Chebyshev
operational matrix technique to solve two-dimensional multi-order
time-fractional partial differential equations; nonlinear and linear in respect
to spatial and temporal variables, respectively. Fractional derivatives are
estimated by Caputo sense. Boundary element method is used to convert the main
problem into a system of a multi-order fractional ordinary differential
equation. Then, the produced system is approximated by Chebyshev operational
matrix technique, ans its condition number is analyzed. Accuracy and efficiency
of the proposed hybrid scheme are demonstrated by solving three different types
of two-dimensional time fractional convection-diffusion equations numerically.
The convergent rates are calculated for different meshing within the boundary
element technique. Numerical results are given by graphs and tables for
solutions and different type of error norms.
