We extend the Kulkarni class of multivariate phase{type distributions
in a natural time{fractional way to construct a new class of multivariate
distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The
approach relies on assigning rewards to a non{Markovian jump process with ML
sojourn times. This new class complements an earlier multivariate ML construction and in contrast to the former also allows for tail dependence. We derive
properties and characterizations of this class, and work out some special cases
that lead to explicit density representations.