Two approaches of N = 2 fractional supersymmetric quantum mechanics of order k are studied in a complementary way. The first one, based on a generalized Weyl-Heisenberg algebra W_k (that comprizes the affine quantum algebra U_q(sl₂) with q^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.