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Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions

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Abstract

In this paper, we obtain formulas of fractional integration (of Marichev– Saigo–Maeda type) of the generalized multi-index Mittag-Leffler functions E γ,κ [(α j ,β j ) m ; z] generalizing 2m-parametric Mittag-Leffler functions studied by Saxena and Nishimoto (J. Fract. Calc. 37 (2010] 43–52). Some interesting special cases of our main results are considered too.

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Acknowledgements

The authors take this opportunity to express their deepest thanks to the worthy referee for his/her valuable comments and suggestions that helped improve this paper in its present form. The work of the second author is partially supported by IMAPS EU PEOPLE IAPP Project PIAP-GA-2009-251475 HYDROFRAC.

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Authors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, 303 012, India

    PRAVEEN AGARWAL & SERGEI V ROGOSIN

  2. Department de Analisis Matemático, Universidad de La Laguna, C/Astr. Fco. Sánchez s/n, 38271, La Laguna Tenerife, Spain

    JUAN J TRUJILLO

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  1. PRAVEEN AGARWAL
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  2. SERGEI V ROGOSIN
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Correspondence to PRAVEEN AGARWAL.

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Communicating Editor: B V Rajarama Bhat

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AGARWAL, P., ROGOSIN, S.V. & TRUJILLO, J.J. Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions. Proc Math Sci 125, 291–306 (2015). https://doi.org/10.1007/s12044-015-0243-6

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