bosonize the supersymmetric quantum mechanics through the realization of $N=2$ superalgebra on the Fock space of the deformed (or ordinary, undeformed) bosonic oscillator. Moreover, we shall show that the two applications of the deformed Heisenberg algebra turn out to be related through the more general OSp(2$|$2) superalgebraic structure.

The paper is organized as follows. In section 2, starting from the presentation of the main idea of the group-theoretical approach, we consider a ‘universal’ (but nonminimal) covariant vector set of linear differential equations for the fractional spin fields [@cor] and formulate the problem of constructing the minimal spinor set of linear differential equations. Such a construction is realized in section 4 with the help of the deformed Heisenberg algebra, which itself is considered in section 3. In the latter section we shall show, in particular, that the Vasiliev deformed bosonic oscillator, given by this algebra, and the q-deformed Arik-Coon [@qac] and Macfarlane-Biedenharn oscillators [@qmb] have a general structure of the generalized deformed oscillator considered in ref. [@qd]. Section 5 is devoted to realization of $N=2$ supersymmetric quantum mechanics on the Fock space of one (ordinary or deformed) bosonic oscillator. First, we realize the simplest superoscillator in terms of creation and annihilation 