Correlated fractional counting processes on a finite time interval

We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in [9]. The main case concerns a class of space-time fractional Poisson processes and, when the correlation parameter is equal to zero, the univariate distributions coincide with the ones of the space-time fractional Poisson process in [24]. On the other hand, when we consider the time fractional Poisson process, the multivariate finite dimensional distributions are different from the ones presented for the renewal process in [26]. Another case concerns a class of fractional negative binomial processes.