S-generalized Mittag-Leffler Function and its Certain Properties

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Mathematical Sciences and Applications E-Notes
Volume:7 Issue:2
S-generalized Mittag-Leffler Function and its Certain Properties

S-generalized Mittag-Leffler Function and its Certain Properties

Authors : Praveen AGARWAL, Aysegul CETİNKAYA, Shilpi JAİN, İ Onur KIYMAZ

Pages : 139-148

Doi:10.36753/mathenot.578638

View : 31 | Download : 8

Publication Date : 2019-10-15

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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.
Keywords : Mittag Leffler function, generalized beta function, fractional derivative

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