Abstract

In the present paper we will establish some results and properties of $q$-generalized Mittag-Leffler function $E_{\alpha,\beta,r}^{\gamma,\delta, s}(z;q)$. We will get its convergence condition, recurrence relation and many other results associated with fractional calculus such as $q$-Laplace transform, Riemann-Liouville fractional $q$-integral operator. We will also discuss some important special cases of main results.

Keywords and Phrases

Generalized $q$-Mittag Leffler Function, $q$-Gamma Function, $q$-Beta Function, $q$-Laplace transform, $q$-Derivative, $q$-Integral.

A.M.S. subject classification

33E12, 33D05, 44A20.

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