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Review | Open Access

A comprehensive review of Grüss-type fractional integral inequality

Muhammad Tariq1( )Sotiris K. Ntouyas2Hijaz Ahmad3,4,5( )Asif Ali Shaikh1,6Bandar Almohsen7Evren Hincal6
Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro 76062, Pakistan
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Kuwait
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Department of Mathematics, Faculty of Arts and Sciences Near East University, Mersin 99138, Turkey
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
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Abstract

A survey of results on Grüss-type inequalities associated with a variety of fractional integral and differential operators is presented. The fractional differential operators includes, Riemann-Liouville fractional integral operators, Riemann-Liouville fractional integrals of a function with respect to another function, Katugampola fractional integral operators, Hadamard's fractional integral operators, k-fractional integral operators, Raina's fractional integral operators, tempered fractional integral operators, conformable fractional integrals operators, proportional fractional integrals operators, generalized Riemann-Liouville fractional integral operators, Caputo-Fabrizio fractional integrals operators, Saigo fractional integral operators, quantum integral operators, and Hilfer fractional differential operators.

CLC number: 26A33, 26A51, 26D07, 26D10, 26D15

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AIMS Mathematics
Pages 2244-2281

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Cite this article:
Tariq M, Ntouyas SK, Ahmad H, et al. A comprehensive review of Grüss-type fractional integral inequality. AIMS Mathematics, 2024, 9(1): 2244-2281. https://doi.org/10.3934/math.2024112

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Received: 23 October 2023
Revised: 28 November 2023
Accepted: 06 December 2023
Published: 15 January 2024
©2024 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)