New classes of unified fractional integral inequalities

Gauhar Rahman; Muhammad Samraiz; Saima Naheed; Artion Kashuri; Kamsing Nonlaopon; Gauhar Rahman; Muhammad Samraiz; Saima Naheed; Artion Kashuri; Kamsing Nonlaopon

doi:10.3934/math.2022853

AIMS Mathematics

2022, Volume 7, Issue 8: 15563-15583. doi: 10.3934/math.2022853

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Research article Special Issues

New classes of unified fractional integral inequalities

1.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2.
Department of Mathematics, University of Sargodha P.O. Box 40100, Sargodha, Pakistan
3.
Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 06 April 2022 Revised: 06 May 2022 Accepted: 09 June 2022 Published: 23 June 2022
MSC : 26A33, 26D10, 26D53

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\in\mathbb{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 $ \hbar $ and $ \Lambda $ available in the literature, many new forms of fractional integral inequalities can be produced.
- fractional integrals,
- fractional proportional integrals,
- fractional integral inequalities
Citation: Gauhar Rahman, Muhammad Samraiz, Saima Naheed, Artion Kashuri, Kamsing Nonlaopon. New classes of unified fractional integral inequalities[J]. AIMS Mathematics, 2022, 7(8): 15563-15583. doi: 10.3934/math.2022853

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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\in\mathbb{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 $ \hbar $ and $ \Lambda $ available in the literature, many new forms of fractional integral inequalities can be produced.

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