S-generalized Mittag-Leffler Function and its Certain Properties

Abstract

In 2014, S-generalized beta function which consist of seven parameters, defined and studied by Srivastava et al. [H. M. Srivastava, P. Agarwal and S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), pp. 348-352]. In this paper, by using S-generalized beta function, we introduce a new generalization of Mittag-Leffler function. This new generalization of Mittag-Leffler function is consist of eleven parameters. We also investigate some of its certain properties such as integral representations, recurrence formulas and derivative formulas by using classical and fractional derivatives. Furthermore, we determine its Mellin, beta and Laplace integral transforms.