We have extended the fractional-dimensional space approach to study exciton
states and diamagnetic shifts in symmetric coupled double
GaAs-Ga1-xAlxAs quantum wells. In this scheme, the fractional
dimension is chosen using an analytical procedure, and the real anisotropic
`exciton + double quantum well' semiconductor system is mapped,
for each exciton state, into an effective fractional-dimensional isotropic
environment. We have performed calculations within the fractional-dimensional
space scheme for the binding energies of 1s-like heavy-hole direct excitons
and for the energy difference between 1s- and 2s-like direct heavy-hole
exciton states in GaAs-Ga1-xAlxAs symmetric coupled
double quantum wells. Also, theoretical results were obtained for the
magnetic-field dependence of the 1s-like heavy-hole exciton energy shift and
for the exciton diamagnetic coefficient in quantum wells and symmetric coupled
double quantum wells. Fractional-dimensional theoretical results are shown to
be in good agreement with available experimental measurements and previous
theoretical calculations.