On generalized fractional integral operator associated with generalized Bessel-Maitland function

Rana Safdar Ali; Saba Batool; Shahid Mubeen; Asad Ali; Gauhar Rahman; Muhammad Samraiz; Kottakkaran Sooppy Nisar; Roshan Noor Mohamed; Rana Safdar Ali; Saba Batool; Shahid Mubeen; Asad Ali; Gauhar Rahman; Muhammad Samraiz; Kottakkaran Sooppy Nisar; Roshan Noor Mohamed

doi:10.3934/math.2022167

AIMS Mathematics

2022, Volume 7, Issue 2: 3027-3046. doi: 10.3934/math.2022167

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On generalized fractional integral operator associated with generalized Bessel-Maitland function

1.
Department of Mathematics, University of Lahore, Lahore, Pakistan
2.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
3.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
4.
Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University Wadi Aldawaser 11991, Saudi Arabia
5.
Department of Pediatric Dentistry, Faculty of Dentistry, Taif University, P.O. box 11099, Taif 21944, Saudi Arabia

Received: 23 September 2021 Accepted: 07 November 2021 Published: 23 November 2021
MSC : 26A33, 44A10

In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.
- extended Bessel-Maitland function,
- integral transform,
- Riemann-Liouville fractional integral operator
Citation: Rana Safdar Ali, Saba Batool, Shahid Mubeen, Asad Ali, Gauhar Rahman, Muhammad Samraiz, Kottakkaran Sooppy Nisar, Roshan Noor Mohamed. On generalized fractional integral operator associated with generalized Bessel-Maitland function[J]. AIMS Mathematics, 2022, 7(2): 3027-3046. doi: 10.3934/math.2022167

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Abstract

In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.

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