  Reflection symmetric Erd$\acute{\text{e}}$lyi-Kober type fractional integral
operators are used to construct fractional quasi-particle generators. The
eigenfunctions and eigenvalues of these operators are given analytically. A set
of fractional creation- and annihilation-operators is defined and the
properties of the corresponding free Hamiltonian are investigated. Analogue to
the classical approach for interacting multi-particle systems the results are
interpreted as a fractional quantum model for a description of residual
interactions of pairing type.
