Fractional Poisson Processes of Order K

08/13/2020

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by   Neha Gupta, et al.

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In this article, we introduce and study time- and space-fractional Poisson processes of order k. These processes are defined in terms of fractional compound Poisson processes. Time-fractional Poisson process of order k naturally generalizes the Poisson process and Poisson process of order k to a heavy tailed waiting times counting process. The space-fractional Poisson process of order k, allows on average infinite number of arrivals in any interval. We derive the marginal probabilities, governing difference-differential equations of the introduced processes.