  It is well known that certain fractional diffusion equations can be solved by
the densities of stable L\'evy motions. In this paper we use the classical
semigroup approach for L\'evy processes to define semi-fractional derivatives,
which allows us to generalize this statement to semistable L\'evy processes. A
Fourier series approach for the periodic part of the corresponding L\'evy
exponents enables us to represent semi-fractional derivatives by a
Gr\"unwald-Letnikov type formula. We use this formula to calculate
semi-fractional derivatives and solutions to semi-fractional diffusion
equations numerically. In particular, by means of the Gr\"unwald-Letnikov type
formula we provide a numerical algorithm to compute semistable densities.
