$(p, q)$-Analogue of Mittag-Leffler Function with $(p, q)$-Laplace Transform (Analysis in Theory and Applications, 2022)
The aim of this paper is to define $(p, q)$-analogue of Mittag-Leffler Function, by using $(p, q)$-Gamma function. Some transformation formulae are also derivedby using the $(p, q)$-derivative. The $(p, q)$-analogue for this function provides elegantgeneralization of $q$-analogue of Mittag-Leffler function in connection with $q$-calculus.Moreover, the $(p, q)$-Laplace Transform of the Mittag-Leffler function has been obtained. Some special cases have also been discussed.
Keywords: $(p; q)$-analogue of Mittag-Leffler function; $(p; q)$-Gamma function; $q$-calculus; q)$-derivative operator; q)$-Laplace transform.