Matrix-Variate Statistical Distributions and Fractional Calculus
Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 138.

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MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA 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 of fractional differential equations, Mittag-Leffler functions and Fox H-function appear naturally. Some results connected with generalized Mittag-Leffler density and their asymptotic behavior will be considered. Reference is made to applications in physics, particularly super statistics and nonextensive statistical mechanics.
Classification : 33E12, 44A20, 62E15, 15B52, 15A15, 33C60, 26A33
Mots-clés : Fractional Calculus, Matrix-Variate Statistical Distributions, Pathway Model, Fox H-Function, Mittag-Leffler Function, Lévy Density, Extended Beta Models, Krätzel Integral, fractional calculus, matrix-variate statistical distributions, pathway model, Fox H-function, Mittag-Leffler function, Lévy density, Krätzel integral, extended beta models 
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Mathai, A.; Haubold, H. Matrix-Variate Statistical Distributions and Fractional Calculus. Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 138. https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219651/