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Research Article | Open Access

On boundedness of fractional integral operators via several kinds of convex functions

Yonghong Liu1, Ghulam Farid2( ), Dina Abuzaid3, Hafsa Yasmeen2
School of Computer Science, Chengdu University, Chengdu, China
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
Department of Mathematics, King Abdul Aziz University, Saudi Arabia
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Abstract

For generalizations of concepts of different fields fractional derivative operators as well as fractional integral operators are useful notions. Our aim in this paper is to discuss boundedness of the integral operators which contain Mittag-Leffler function in their kernels. The results are obtained for strongly ( α , h − m )-convex functions which hold for different kinds of convex functions at the same time. They also give improvements/refinements of many already published results.

Keywords

strongly (α, h − m)-convex functiongeneralized fractional integral operatorsunified Mittag-Leffler functionbounds
CLC number: 26A33, 26D10, 31A10

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AIMS Mathematics
Volume 7 Issue 10,
October 2022
Pages 19167-19179
DOI: 10.3934/math.20221052

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Cite this article:
Liu Y, Farid G, Abuzaid D, et al. On boundedness of fractional integral operators via several kinds of convex functions. AIMS Mathematics, 2022, 7(10): 19167-19179. https://doi.org/10.3934/math.20221052

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Received: 26 June 2022
Revised: 17 August 2022
Accepted: 23 August 2022
Published: 15 October 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)