Fractional Calculus Matrix-Variate Statistical Distributions Pathway Model Fox H-Function Mittag-Leffler Function Lévy Density Extended Beta Models Krätzel Integral
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 14, No 1, (2011), 138p-155p
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.
MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday