  Fractional calculus and q-deformed Lie algebras are closely related. Both
concepts expand the scope of standard Lie algebras to describe generalized
symmetries. For the fractional harmonic oscillator, the corresponding q-number
is derived. It is shown, that the resulting energy spectrum is an appropriate
tool e.g. to describe the ground state spectra of even-even nuclei. In
addition, the equivalence of rotational and vibrational spectra for fractional
q-deformed Lie algebras is shown and the $B_\alpha(E2)$ values for the
fractional q-deformed symmetric rotor are calculated.

General Physics