Multivariate Mittag-Leffler function and related fractional integral operators

Author:

Rahman Gauhar1,Samraiz Muhammad2,Alqudah Manar A.3,Abdeljawad Thabet456

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference42 articles.

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3. I. Podlubny, Fractional differential equations, London: Academic Press, 1999.

4. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives: theory and applications, Switzerland: Gordon and Breach, 1993.

5. I. Ahmad, H. Ahmad, M. Inc, S. W. Yao, B. Almohsen, Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer, Therm. Sci., 24 (2020), 95–105. https://doi.org/10.2298/TSCI20S1095A

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