A thorough detailed study of donor and acceptor properties in doped GaAs-(Ga,Al)As semiconductor superlattices is performed within the fractional-dimensional approach, in which the real anisotropic 'impurity+semiconductor superlattice' system is modeled through an effective isotropic environment with a fractional dimension. In this scheme, the fractional-dimensional parameter is chosen via an analytical procedure and involves no ansatz, and no fittings either with experiment or with previous variational calculations. The present fractional-dimensional calculated results for the donor and acceptor energies in GaAs-(Ga,Al)As semiconductor superlattices are found in quite good agreement with previous variational calculations and available experimental measurements. (C) 1999 American Institute of Physics. [S0021-8979(99)04408-4].858140454049