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Research Article | Open Access

New classes of unified fractional integral inequalities

Gauhar Rahman1Muhammad Samraiz2Saima Naheed2Artion Kashuri3Kamsing Nonlaopon4( )
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
Department of Mathematics, University of Sargodha P.O. Box 40100, Sargodha, Pakistan
Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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Abstract

Many researchers in recent years have studied fractional integrals and derivatives. Some authors recently introduced generalized fractional integrals, the so-called unified fractional integrals. In this article, we establish certain new integral inequalities by employing the unified fractional integral operators. In fact, for a class of n ( n N ) , positive continuous and decreasing functions on [ v 1 , v 2 ] , certain new classes of integral inequalities are discussed. The inequalities established in this manuscript are more general forms of the classical inequalities given in the literature. The existing classical inequalities can be rectified by imposing the conditions stated in remarks. By imposing certain conditions on and Λ available in the literature, many new forms of fractional integral inequalities can be produced.

CLC number: 26A33, 26D10, 26D53

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AIMS Mathematics
Pages 15563-15583

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Cite this article:
Rahman G, Samraiz M, Naheed S, et al. New classes of unified fractional integral inequalities. AIMS Mathematics, 2022, 7(8): 15563-15583. https://doi.org/10.3934/math.2022853

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Received: 06 April 2022
Revised: 06 May 2022
Accepted: 09 June 2022
Published: 15 August 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)