  In this paper we introduce a Fock space related to derivatives of
Gelfond-Leontiev type, a class of derivatives which includes many classic
examples like fractional derivatives or Dunkl operators. For this space we
establish a modified Bargmann transform as well as density theorems for
sampling and interpolation. These density theorems allow us to establish
lattice conditions for the construction of frames arising from integral
transforms which are linked by the modified Bargmann transform with the Fock
space.
