S-generalized Mittag-Leffler Function and its Certain Properties

Year 2019, Volume: 7 Issue: 2, 139 - 148, 15.10.2019

Praveen Agarwal , Aysegul Cetinkaya , Shilpi Jain İ. Onur Kıymaz

https://doi.org/10.36753/mathenot.578638

Cited By: 2

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.  

Keywords

Mittag-Leffler function, generalized beta function, fractional derivative

Supporting Institution

Department of Science \& Technology(DST), India and Science \& Engineering Research Board (SERB), India

Project Number

INT/RUS/RFBR/P-308 and TAR/2018/000001

Thanks

The research was supported by the Department of Science \& Technology(DST), India (No:INT/RUS/RFBR/P-308) and Science \& Engineering Research Board (SERB), India (No:TAR/2018/000001).

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