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A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus

Author

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  • Rakesh K. Parmar

    (Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, India)

Abstract

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leffler function by means of the extended Beta function. We then systematically investigate several properties of the extended Mittag–Leffler function, including, for example, certain basic properties, Laplace transform, Mellin transform and Euler-Beta transform. Further, certain properties of the Riemann–Liouville fractional integrals and derivatives associated with the extended Mittag–Leffler function are investigated. Some interesting special cases of our main results are also pointed out.

Suggested Citation

  • Rakesh K. Parmar, 2015. "A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus," Mathematics, MDPI, vol. 3(4), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:4:p:1069-1082:d:58428
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    References listed on IDEAS

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    1. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
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    Cited by:

    1. F. Ghanim & Hiba F. Al-Janaby & Marwan Al-Momani & Belal Batiha, 2022. "Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    2. Tayyaba Manzoor & Adnan Khan & Kahsay Godifey Wubneh & Hafte Amsalu Kahsay, 2021. "Beta Operator with Caputo Marichev‐Saigo‐Maeda Fractional Differential Operator of Extended Mittag‐Leffler Function," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).

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