  In this paper, we study loaded modified diffusion equation (the Hallaire
equation with the fractional derivative with respect to time). The compact
finite difference scheme of Crank-Nicholson type of higher order is developed
for approximating the stated problem on uniform grids. A priori estimates are
obtained in difference and differential interpretations, from which there
follow uniqueness, stability, and convergence of the solution of the difference
problem to solution of the differential problem with the rate
$\mathcal{O}(h^4+\tau^{2-\alpha}.)$ Proposed theoretical calculations are
confirmed by numerical experiments on test problem.
