fractional spin fields, and it is necessary to find out more convenient set of linear differential equations, which would be a starting point for a subsequent realization of the program described above.

In the recent paper [@cor], the following covariant vector set of linear differential equations for a field with arbitrary fractional spin has been constructed by the author and J.L. Cortés: $$\begin{aligned}
&V_{\mu}\Psi=0,&
\label{vector}\\
&V_{\mu}=\alpha P_{\mu}-i\epsilon_{\mu\nu\lambda}P^{\nu}J^{\lambda}
+\varepsilon mJ_{\mu},&
\label{lvector}\end{aligned}$$ where $\varepsilon=\pm 1$, and we suppose that $\alpha$ is an arbitrary dimensionless parameter. This set of three equations has the following remarkable property. From the very beginning one can suppose only that $J_{\mu}$ are the generators of the (2+1)-dimensional Lorentz group satisfying commutation relations (\[alg\]), not fixing at all the choice of the concrete (reducible or irreducible) representation. Then, multiplying eqs. (\[vector\]) by the operators $J_{\mu}$, $P_{\mu}$ and $\epsilon_{\mu\nu\lambda}P^{\nu}J^{\lambda}$, we arrive at the Klein-Gordon equation (\[kle\]) and Majorana-type equation (\[maj\]) with $s=\varepsilon\alpha$ as a consequence of the initial system of equations (\[vector\]), and moreover, we also find that the equation $$(J^2 +\alpha(\alpha-1))\Psi=0
\label{irr}$$ is a consequence of eqs. (\[vector\]). Eq. (\[irr\]) is nothing else as the condition of irreducibility of corresponding representation. When $\alpha>0$, the system of eqs. (\[kle\]), (\[maj\]) 