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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia

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Generalization of the fractional poisson distribution

1GigaHedron, Berliner Ring 80 D - 63303 Dreieich, Germany

Citation Information: Fractional Calculus and Applied Analysis. Volume 19, Issue 4, Pages 832–842, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2016-0045, August 2016

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A generalization of the Poisson distribution based on the generalized Mittag-Leffler function Eα,β(λ) is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that the proposed distribution function contains the standard fractional Poisson distribution as a subset. A possible interpretation of the additional parameter β is suggested.

MSC 2010: Primary 26A33; Secondary 33E12, 60EXX, 11B73

Key Words and Phrases: fractional calculus; Mittag-Leffler functions; fractional Poisson distribution; Bell polynomials; Stirling numbers

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