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Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathai, A. — 2010

Fractional Calculus and Applied Analysis

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15. Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler...

Matrix-Variate Statistical Distributions and Fractional Calculus

Mathai, A.;  Haubold, H. — 2011

Fractional Calculus and Applied Analysis

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions...

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