Dergiler / Mathematical Sciences and Applications E-Notes / 2019 / Cilt: 7 - Sayı: 2
S-generalized Mittag-Leffler Function and its Certain Properties
- Sayfa
- 139–148
- DOI
- —
Abstract
In 2014, S-generalized beta function which consist ofseven parameters, defined and studied by Srivastava et al. [H. M.Srivastava, P. Agarwal and S. Jain, Generating functions for thegeneralized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), pp. 348-352]. In this paper, by using S-generalizedbeta function, we introduce a new generalization of Mittag-Lefflerfunction. This new generalization of Mittag-Leffler function is consist of eleven parameters. We also investigate some of its certainproperties such as integral representations, recurrence formulas andderivative formulas by using classical and fractional derivatives.Furthermore, we determine its Mellin, beta and Laplace integraltransforms.