Two complementary approaches of N = 2 fractional supersymmetric quantum
mechanics of order k are studied in this article. The first one, based on a
generalized Weyl-Heisenberg algebra W(k) (that comprizes the affine quantum
algebra Uq(sl(2)) with q to k = 1 as a special case), apparently contains
solely one bosonic degree of freedom. The second one uses generalized bosonic
and k-fermionic degrees of freedom. As an illustration, a particular emphasis
is put on the fractional supersymmetric oscillator of order k.Comment: 25 pages, LaTex file, based on a talk given by M. Kibler at the "IX
International Conference on Symmetry Methods in Physics" (Yerevan, Armenia,
3-8 July 2001) organized by the Joint Institute for Nuclear Research (Dubna,
Russia) and the Yerevan State University (Yerevan, Armenia