Multivariate Mittag-Leffler function and related fractional integral operators

Gauhar Rahman; Muhammad Samraiz; Manar A. Alqudah; Thabet Abdeljawad; Gauhar Rahman; Muhammad Samraiz; Manar A. Alqudah; Thabet Abdeljawad

doi:10.3934/math.2023671

AIMS Mathematics

2023, Volume 8, Issue 6: 13276-13293. doi: 10.3934/math.2023671

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Research article

Multivariate Mittag-Leffler function and related fractional integral operators

1.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2.
Department of Mathematics, University of Sargodha, P. O. Box, 40100, Sargodha, Pakistan
3.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah bint Abdulrahman University, P. O. Box, 84428, Riyadh 11671, Saudi Arabia
4.
Department of Mathematics and Sciences, Prince Sultan University, P. O. Box, 66833, Riyadh 11586, Saudi Arabia
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

Received: 09 February 2023 Revised: 19 March 2023 Accepted: 20 March 2023 Published: 04 April 2023
MSC : 26A33, 33E12

In this paper, we describe a new generalization of the multivariate Mittag-Leffler (M-L) function in terms of generalized Pochhammer symbol and study its properties. We provide a few differential and fractional integral formulas for the generalized multivariate M-L function. Furthermore, by using the generalized multivariate M-L function in the kernel, we present a new generalization of the fractional integral operator. Finally, we describe some fundamental characteristics of generalized fractional integrals.
- multivariate Mittag-Leffler,
- generalized pochhammer symbol,
- fractional integrals
Citation: Gauhar Rahman, Muhammad Samraiz, Manar A. Alqudah, Thabet Abdeljawad. Multivariate Mittag-Leffler function and related fractional integral operators[J]. AIMS Mathematics, 2023, 8(6): 13276-13293. doi: 10.3934/math.2023671

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Abstract

In this paper, we describe a new generalization of the multivariate Mittag-Leffler (M-L) function in terms of generalized Pochhammer symbol and study its properties. We provide a few differential and fractional integral formulas for the generalized multivariate M-L function. Furthermore, by using the generalized multivariate M-L function in the kernel, we present a new generalization of the fractional integral operator. Finally, we describe some fundamental characteristics of generalized fractional integrals.

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