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Research Article | Open Access

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

Rana Safdar Ali1, Saba Batool1, Shahid Mubeen2, Asad Ali3, Gauhar Rahman3, Muhammad Samraiz2, Kottakkaran Sooppy Nisar4( ), Roshan Noor Mohamed5
Department of Mathematics, University of Lahore, Lahore, Pakistan
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University Wadi Aldawaser 11991, Saudi Arabia
Department of Pediatric Dentistry, Faculty of Dentistry, Taif University, P.O. box 11099, Taif 21944, Saudi Arabia
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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.

Keywords

extended Bessel-Maitland functionintegral transformRiemann-Liouville fractional integral operator
CLC number: 26A33, 44A10

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 3027-3046
DOI: 10.3934/math.2022167

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Cite this article:
Ali RS, Batool S, Mubeen S, et al. On generalized fractional integral operator associated with generalized Bessel-Maitland function. AIMS Mathematics, 2022, 7(2): 3027-3046. https://doi.org/10.3934/math.2022167

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Received: 23 September 2021
Accepted: 07 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)