  Quantum dots in the fractional quantum Hall regime are studied using a
Hartree formulation of composite fermion theory. Under appropriate conditions
the chemical potential of the dots will oscillate periodically with B due to
the transfer of composite fermions between quasi-Landau bands. This effect is
analogous to the addition spectrum oscillations which occur in quantum dots in
the integer quantum Hall regime. Period phi_0 oscillations are found in sharply
confined dots with filling factors nu=2/5 and nu=2/3. Period 3*phi_0
oscillations are found in a parabolically confined nu=2/5 dot. More generally,
we argue that the oscillation period of dots with band pinning should vary
continuously with B whereas the period of dots without band pinning is phi_0.
Finally, we discuss the possibility of detecting fractionally charged
excitations using the observed period of addition spectrum oscillations.
