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Research Article | Open Access

Generalized inequalities involving fractional operators of the Riemann-Liouville type

Paul Bosch1, Héctor J. Carmenate2, José M. Rodríguez3, José M. Sigarreta4( )
Facultad de Ingeniería, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago 7550000, Chile
Centro Acapulco, Facultad de Matemática, Universidad Autónoma de Guerrero, Acapulco de Juárez, Guerrero 39610, Mexico
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, Madrid 28911, España
Centro Acapulco, Facultad de Matemática, Universidad Autónoma de Guerrero, Acapulco de Juárez, Guerrero 39610, Mexico
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Abstract

In this paper, we present a general formulation of the well-known fractional drifts of Riemann-Liouville type. We state the main properties of these integral operators. Besides, we study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving these general fractional operators.

Keywords

fractional derivatives and integralsOstrowski inequalitySzékely-Clark-Entringer inequalityHermite-Hadamard-Fejér inequality
CLC number: 26A33, 26D07, 34A08, 34C11

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 1470-1485
DOI: 10.3934/math.2022087

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Cite this article:
Bosch P, Carmenate HJ, Rodríguez JM, et al. Generalized inequalities involving fractional operators of the Riemann-Liouville type. AIMS Mathematics, 2022, 7(1): 1470-1485. https://doi.org/10.3934/math.2022087

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Received: 25 July 2021
Accepted: 17 October 2021
Published: 15 January 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)