  In this paper, we introduce a generalized fractional negative binomial
process (GFNBP) by time changing the fractional Poisson process with an
independent Mittag-Leffler (ML) Levy subordinator. We study its distributional
properties and its connection to PDEs. We examine the long-range dependence
(LRD) property of the GFNBP and show that it is not infinitely divisible. The
space fractional and the non-homogeneous variants of the GFNBP are explored.
Finally, simulated sample paths for the ML Levy subordinator and the GFNBP are
also presented.
