SOME PROPERTIES OF $q-$ANALOGUE OF GENERALIZED MITTAG-LEFFLER FUNCTION ASSOCIATED WITH FRACTIONAL CALCULUS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 148
DOI:
Author :
Krishna Gopal Bhadana (Department of Mathematics, SPC Government College, Ajmer, Rajasthan, Maharshi Dayanand Saraswati University, Ajmer, Rajasthan - 305001, INDIA)
Ashok Kumar Meena (Department of Mathematics, SPC Government College, Ajmer, Rajasthan, Maharshi Dayanand Saraswati University, Ajmer, Rajasthan - 305001, INDIA)
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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