Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities
Ostrowski inequality provides the estimation of a function to its integral mean. It is useful in error estimations of quadrature rules in numerical analysis. The objective of this paper is to define a more general form of Riemann-Liouville k-fractional integrals with respect to an increasing functio...
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| Format: | Article |
| Language: | English |
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IEEE
2018-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8513755/ |
| _version_ | 1819163184080093184 |
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| author | Young Chel Kwun Ghulam Farid Waqas Nazeer Saleem Ullah Shin Min Kang |
| author_facet | Young Chel Kwun Ghulam Farid Waqas Nazeer Saleem Ullah Shin Min Kang |
| author_sort | Young Chel Kwun |
| collection | DOAJ |
| description | Ostrowski inequality provides the estimation of a function to its integral mean. It is useful in error estimations of quadrature rules in numerical analysis. The objective of this paper is to define a more general form of Riemann-Liouville k-fractional integrals with respect to an increasing function, which are used to obtain fractional integral inequalities of Ostrowski type. A simple and straightforward approach is followed to establish these inequalities. The applications of established results are also briefly discussed and succeeded to get bounds of some fractional Hadamard inequalities. |
| first_indexed | 2024-12-22T17:40:05Z |
| format | Article |
| id | doaj.art-533cdc01236545918f4e9c9cfa866b1a |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T17:40:05Z |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-533cdc01236545918f4e9c9cfa866b1a2022-12-21T18:18:26ZengIEEEIEEE Access2169-35362018-01-016649466495310.1109/ACCESS.2018.28782668513755Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard InequalitiesYoung Chel Kwun0Ghulam Farid1Waqas Nazeer2Saleem Ullah3Shin Min Kang4Department of Mathematics, Dong-A University, Busan, South KoreaDepartment of Mathematics, Attock Campus, COMSATS University Islamabad, Attock, PakistanDivision of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, Air University, Islamabad, PakistanDepartment of Mathematics and RINS, Gyeongsang National University, Jinju, South KoreaOstrowski inequality provides the estimation of a function to its integral mean. It is useful in error estimations of quadrature rules in numerical analysis. The objective of this paper is to define a more general form of Riemann-Liouville k-fractional integrals with respect to an increasing function, which are used to obtain fractional integral inequalities of Ostrowski type. A simple and straightforward approach is followed to establish these inequalities. The applications of established results are also briefly discussed and succeeded to get bounds of some fractional Hadamard inequalities.https://ieeexplore.ieee.org/document/8513755/Fractional inequalitiesHadamard inequalityOstrowski inequalityRiemann-Liouville fractional integralsGeneralized fractional integrals |
| spellingShingle | Young Chel Kwun Ghulam Farid Waqas Nazeer Saleem Ullah Shin Min Kang Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities IEEE Access Fractional inequalities Hadamard inequality Ostrowski inequality Riemann-Liouville fractional integrals Generalized fractional integrals |
| title | Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities |
| title_full | Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities |
| title_fullStr | Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities |
| title_full_unstemmed | Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities |
| title_short | Generalized Riemann-Liouville <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities |
| title_sort | generalized riemann liouville inline formula tex math notation latex k tex math inline formula fractional integrals associated with ostrowski type inequalities and error bounds of hadamard inequalities |
| topic | Fractional inequalities Hadamard inequality Ostrowski inequality Riemann-Liouville fractional integrals Generalized fractional integrals |
| url | https://ieeexplore.ieee.org/document/8513755/ |
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