A basic study of a fractional integral operator with extended Mittag-Leffler kernel

Gauhar Rahman; Iyad Suwan; Kottakkaran Sooppy Nisar; Thabet Abdeljawad; Muhammad Samraiz; Asad Ali; Gauhar Rahman; Iyad Suwan; Kottakkaran Sooppy Nisar; Thabet Abdeljawad; Muhammad Samraiz; Asad Ali

doi:10.3934/math.2021736

AIMS Mathematics

2021, Volume 6, Issue 11: 12757-12770. doi: 10.3934/math.2021736

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A basic study of a fractional integral operator with extended Mittag-Leffler kernel

1.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2.
Department of Mathematics and Statistics, The Arab American University, P.O. Box 240, 13 Zababdeh, Jenin, Palestine
3.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawser 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
4.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, KSA
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
6.
Samraiz-Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan

Received: 29 July 2021 Accepted: 29 August 2021 Published: 07 September 2021
MSC : 26A33, 26D10, 26D53, 05A30

In this present paper, the basic properties of an extended Mittag-Leffler function are studied. We present some fractional integral and differential formulas of an extended Mittag-Leffler function. In addition, we introduce a new extension of Prabhakar type fractional integrals with an extended Mittag-Leffler function in the kernel. Also, we present certain basic properties of the generalized Prabhakar type fractional integrals.
- Mittag-Leffler function,
- fractional integral,
- Prabhakar fractional integral
Citation: Gauhar Rahman, Iyad Suwan, Kottakkaran Sooppy Nisar, Thabet Abdeljawad, Muhammad Samraiz, Asad Ali. A basic study of a fractional integral operator with extended Mittag-Leffler kernel[J]. AIMS Mathematics, 2021, 6(11): 12757-12770. doi: 10.3934/math.2021736

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Abstract

In this present paper, the basic properties of an extended Mittag-Leffler function are studied. We present some fractional integral and differential formulas of an extended Mittag-Leffler function. In addition, we introduce a new extension of Prabhakar type fractional integrals with an extended Mittag-Leffler function in the kernel. Also, we present certain basic properties of the generalized Prabhakar type fractional integrals.

References

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