Generalized inequalities involving fractional operators of the Riemann-Liouville type

Paul Bosch; Héctor J. Carmenate; José M. Rodríguez; José M. Sigarreta; Paul Bosch; Héctor J. Carmenate; José M. Rodríguez; José M. Sigarreta

doi:10.3934/math.2022087

AIMS Mathematics

2022, Volume 7, Issue 1: 1470-1485. doi: 10.3934/math.2022087

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Research article

Generalized inequalities involving fractional operators of the Riemann-Liouville type

1.
Facultad de Ingeniería, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago 7550000, Chile
2.
Centro Acapulco, Facultad de Matemática, Universidad Autónoma de Guerrero, Acapulco de Juárez, Guerrero 39610, Mexico
3.
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, Madrid 28911, España
4.
Centro Acapulco, Facultad de Matemática, Universidad Autónoma de Guerrero, Acapulco de Juárez, Guerrero 39610, Mexico

Received: 25 July 2021 Accepted: 17 October 2021 Published: 27 October 2021
MSC : 26A33, 26D07, 34A08, 34C11

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.
- fractional derivatives and integrals,
- Ostrowski inequality,
- Székely-Clark-Entringer inequality,
- Hermite-Hadamard-Fejér inequality
Citation: Paul Bosch, Héctor J. Carmenate, José M. Rodríguez, José M. Sigarreta. Generalized inequalities involving fractional operators of the Riemann-Liouville type[J]. AIMS Mathematics, 2022, 7(1): 1470-1485. doi: 10.3934/math.2022087

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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.

References

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