Abstract
In this paper we consider the differential-difference reflection operator associated with a finite cyclic group,
First we show that the Dimovski ([
], [
]) hyper–Bessel differential operator of arbitrary integer order
is close in frame of the algebra similar to
(sl(2;C)). Secondly, we introduce a difference-differential operator associated to finite cyclic group in the rank one case, and then by using a Poisson-type integral transform proposed by Dimovski and Kiryakova ([
], [
]), we construct a new explicit intertwining (transmutation) operator between the operator
and the derivative operator
It is to emphasize that both hyper–Bessel operators and the so-called Poisson–Dimovski transformation (transmutation) are typical examples of the operators of generalized fractional calculus [
,
].