  This paper develops a two-level fourth-order scheme for solving
time-fractional convection-diffusion-reaction equation with variable
coefficients subjected to suitable initial and boundary conditions. The basis
properties of the new approach are investigated and both stability and error
estimates of the proposed numerical scheme are deeply analyzed in the
$L^{\infty}(0,T;L^{2})$-norm. The theory indicates that the method is
unconditionally stable with convergence of order
$O(k^{2-\frac{\lambda}{2}}+h^{4})$, where $k$ and $h$ are time step and mesh
size, respectively, and $\lambda\in(0,1)$. This result suggests that the
two-level fourth-order technique is more efficient than a large class of
numerical techniques widely studied in the literature for the considered
problem. Some numerical evidences are provided to verify the unconditional
stability and convergence rate of the proposed algorithm.
