the fractional spin fields within the framework of the group-theoretical approach. So, calling fractional spin fields as anyons, we bear in mind such a hypothetical spin-statistics relation.

Here, we shall consider the problem of constructing the minimal covariant set of linear differential equations for (2+1)-dimensional fractional spin fields within a framework of the group-theoretical approach to anyons, developing the investigation initiated in refs. [@cor; @pld]. We shall see that the minimal set of linear differential equations plays for anyons the role analogous to the role played by the Dirac and Jackiw-Templeton-Schonfield equations [@jts] in the cases of the spinor and topologically massive vector gauge fields, respectively. At the same time, these linear differential equations are similar to the (3+1)-dimensional Dirac positive-energy relativistic wave equations [@dirac]. As it has been declared above, the construction will be realized with the help of the deformed Heisenberg algebra [@vas]. This algebra involves the so called Klein operator as an essential object, which introduces $Z_{2}$-grading structure on the Fock space of the deformed bosonic oscillator. Such a structure, in turn, is an essential ingredient of the supersymmetry considered in ref. [@mac] as a hidden supersymmetry of the deformed bosonic oscillator. Using this observation, we shall 