On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities-Reference-Cited by-同舟云学术

On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities

Published:2023-08-17 Issue:16 Volume:11 Page:3565
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Galeano Delgado Juan Gabriel¹^ORCID,Nápoles Valdés Juan Eduardo²³^ORCID,Pérez Reyes Edgardo Enrique¹^ORCID

Affiliation:

1. Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, Colombia

2. UNNE, FaCENA, Av. Libertad 5450, Corrientes 3400, Argentina

3. UTN-FRRE, Resistencia, Chaco 3500, Argentina

Abstract

In this paper, we present a general formulation of the Riemann–Liouville fractional operator with generalized kernels. Many of the known operators are shown to be particular cases of the one we present. In this new framework, we prove several known integral inequalities in the literature.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/16/3565/pdf

Reference28 articles.

1. Hardy, G.H., Littlewood, J.E., and Pólya, G. (1934). Inequalities, Cambridge University Press.

2. New Hermite-Hadamard inequalities in the framework of generalized fractional integrals;Galeano;Ann. Univ. Craiova Math. Comput. Sci. Ser.,2021

3. Certain integral inequalities of Hermite-Hadamard type for h-convex functions;Galeano;JMCSA,2021

4. Several integral inequalities for generalized Riemann–Liouville fractional operators;Galeano;Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.,2021

5. A note on some integral inequalities in a generalized framework;Galeano;IJAMAS,2021

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