Geodesic
Matrix-Variate Statistical Distributions and Fractional Calculus
Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 138-155

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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 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.
Keywords: Fractional Calculus, Matrix-Variate Statistical Distributions, Pathway Model, Fox H-Function, Mittag-Leffler Function, Lévy Density, Extended Beta Models, Krätzel Integral 
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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, pp. 138-155. http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a8/