Generalized q-Mittag-Leffler Matrix Function and its Properties

Motivated essentially by the success of the applications of the Mittag-Leffler functions and Matrix theory in Science and Engineering, we propose here a unification of certain q-extensions of generalizations of Mittag-Leffler function together with Saxena-Nishimoto's function, Bessel-Maitland function, Dotsenko function, Elliptic Function, etc. We obtain Mellin-Barnes contour integral representation, a q-difference equation, Eigen function property.