Special Functions: Fractional Calculus and the Pathway for Entropy

© 2019 by the authors; CC BY license

special functions; fractional calculus; entropic functional; mathematical physics; applied analysis; statistical distributions; geometrical probabilities; multivariate analysis; hyperbolic series expansion; Carlson’s modern notation; hyperbolic modular function; Möbius transformation; Schwarz-Christoffel transformation; Peeta function; sample correlation coefficient; hypergeometric function; density function; moments; renewal process; Continuous Time Random Walk; erlang process; Mittag-Leffler function; wright function; fractional Poisson process; stable distributions; stable and inverse stable subordinator; diffusion limit; generalized Mittag–Leffler density and process; gamma density; Lévi density; pathway model; Tsallis statistics; superstatistics; fractional integrals; statistical distributions; Bessel function; gamma model; kinetic equation; fractional derivatives and integrals; Mellin convolution; G-function; Mittag-Lefler function; pathway model; entropy measure; superstatistics; Tsallis statistics; beta family; generalized gamma; Dirichlet densities; λ-criterion; H- function; quadratic forms; generalized type-1 Dirichlet model; marginal density; Meijer’s G-function; moments; Caputo fractional derivative; Riesz fractional derivative; α-fractional diffusion equation; Mellin transform; fundamental solution; Mellin-Barnes integrals; entropy; entropy production rate; generalized logistic distribution; normal distribution; Student-t distribution; skew distributions; complex systems; statistical mechanics; non-additive entropies; ergodicity breakdown; convolution property; G-transform; Gauss hypergeometric function; generalized kinetic equation; Laplace transform; Mittag–Leffler function; versatile integral; Guyer-Krumhansl equation; Cattaneo equation; heat propagation; analytical solution; inverse differential operator; Hermite polynomials; inverse operator; derivative; differential equation; special functions; Hermite and Laguerre polynomials; pathway model; multivariate extended gamma density; moments; ARFIMA; long range dependence; fractional order; survey; Mathieu series; generalized Mathieuseries; fractional calculus operators