The convergence of a compact finite difference scheme for one- and twodimensional time fractional fourth order equations with the first Dirichlet boundary
conditions is studied. In one-dimensional case, a Hermite interpolating polynomial is
used to transform the boundary conditions into the homogeneous ones. The Stephenson
scheme is employed for the spatial derivatives discretisation. The approximate values of
the normal derivative are obtained as a by-product of the method. For periodic problems,
the stability of the method and its convergence with the accuracy θ (τ2−α) + θ (h4) are
established, with the similar error estimates for two-dimensional problems. The results
of numerical experiments are consistent with the theoretical findings.