We have extended the fractional-dimensional space approach to study excitonstates and diamagnetic shifts in symmetric coupled double GaAs-Ga1-xAlxAs quantum wells. In this scheme, the fractionaldimension 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 isotropicenvironment. We have performed calculations within the fractional-dimensionalspace scheme for the binding energies of 1s-like heavy-hole direct excitonsand for the energy difference between 1s- and 2s-like direct heavy-holeexciton states in GaAs-Ga1-xAlxAs symmetric coupleddouble quantum wells. Also, theoretical results were obtained for themagnetic-field dependence of the 1s-like heavy-hole exciton energy shift andfor the exciton diamagnetic coefficient in quantum wells and symmetric coupleddouble quantum wells. Fractional-dimensional theoretical results are shown tobe in good agreement with available experimental measurements and previoustheoretical calculations.