  In this work, we consider the Dunkl complex reflection operators related to
the group $G(m,1,N)$ in the complex plane \begin{align*}
T_i=\frac{\partial}{\partial z_i}+k_0\sum_{j\neq
i}\sum_{r=0}^{m-1}\frac{1-s_i^{-r}(i,j)s_i^r} {z_i-\varepsilon^r
z_j}+\sum_{j=1}^{m-1}k_j\sum_{r=0}^{m-1}\frac{\varepsilon^{-rj}s_i^r}{z_i},
\,\,1\leq i\leq N. \end{align*} We first review the theory of Dunkl operators
for complex reflection groups we recall some results related to the
hyper--Bessel functions, which are solutions of a higher order differential
equation. Secondly, we construct a new explicit intertwining operator between
the operator $T_i$ and the partial derivative operator
$\frac{\partial}{\partial x_i}.$ As application we given an explicit solution
of the system: $$ T_if(x)=\kappa\lambda_i f(x),\,\,\, f(0)=1.$$
