On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities
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.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3565 |
| _version_ | 1797583992994660352 |
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| author | Juan Gabriel Galeano Delgado Juan Eduardo Nápoles Valdés Edgardo Enrique Pérez Reyes |
| author_facet | Juan Gabriel Galeano Delgado Juan Eduardo Nápoles Valdés Edgardo Enrique Pérez Reyes |
| author_sort | Juan Gabriel Galeano Delgado |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:46:02Z |
| format | Article |
| id | doaj.art-ddb892c28ea8437f8ee49072e69de676 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:46:02Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ddb892c28ea8437f8ee49072e69de6762023-11-19T02:03:52ZengMDPI AGMathematics2227-73902023-08-011116356510.3390/math11163565On a General Formulation of the Riemann–Liouville Fractional Operator and Related InequalitiesJuan Gabriel Galeano Delgado0Juan Eduardo Nápoles Valdés1Edgardo Enrique Pérez Reyes2Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, ColombiaUNNE, FaCENA, Av. Libertad 5450, Corrientes 3400, ArgentinaDepartamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, ColombiaIn 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.https://www.mdpi.com/2227-7390/11/16/3565generalized fractional Riemann–Liouville integralfractional integral inequalitysynchronous functions |
| spellingShingle | Juan Gabriel Galeano Delgado Juan Eduardo Nápoles Valdés Edgardo Enrique Pérez Reyes On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities Mathematics generalized fractional Riemann–Liouville integral fractional integral inequality synchronous functions |
| title | On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities |
| title_full | On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities |
| title_fullStr | On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities |
| title_full_unstemmed | On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities |
| title_short | On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities |
| title_sort | on a general formulation of the riemann liouville fractional operator and related inequalities |
| topic | generalized fractional Riemann–Liouville integral fractional integral inequality synchronous functions |
| url | https://www.mdpi.com/2227-7390/11/16/3565 |
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