Matrix-Variate Statistical Distributions and Fractional Calculus

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 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.