Tempered Fractional Poisson Processes and Fractional Equations with Z-Transform

Neha Gupta; Arun Kumar; Nikolai Leonenko

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arXiv · 1808.00759

Tempered Fractional Poisson Processes and Fractional Equations with Z-Transform

Neha Gupta·Arun Kumar·Nikolai Leonenko

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Abstract

In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes. We also introduce Gegenbauer type fractional differential equations and their solutions using z-transform. Our results generalize and complement the result available on fractional Poisson processes in several directions.

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Neha Gupta, Arun Kumar, Nikolai Leonenko. 2018-08-02. Tempered Fractional Poisson Processes and Fractional Equations with Z-Transform. https://arxiv.org/abs/1808.00759

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