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Journals / Mathematical Sciences and Applications E-Notes / 2019 / Cilt: 7 - Sayı: 2

S-generalized Mittag-Leffler Function and its Certain Properties

Praveen AGARWAL
Ayşegül ÇETİNKAYA
Shilpi JAIN
I. Onur KIYMAZ
Pages
139–148
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis:In 2014, S-generalized beta function which consist ofseven parameters, defined and studied by Srivastava et al. [H.
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Key Findings & Data:Comput., 247 (2014), pp. 348-352].
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:2014 Verileri
⚙️Variables:Mittag-Leffler function · generalized beta function · fractional derivative

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.

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Cite This Article

AGARWAL, P., ÇETİNKAYA, A., JAIN, S., KIYMAZ, I. O. (2019). S-generalized Mittag-Leffler Function and its Certain Properties. Mathematical Sciences and Applications E-Notes, Cilt: 7 - Sayı: 2, 139–148. https://ajindex.com/articles/283486

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References (2)

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