New estimates considering the generalized proportional Hadamard fractional integral operators
Abstract In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced n...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02730-w |
| _version_ | 1818413272898994176 |
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| author | Shuang-Shuang Zhou Saima Rashid Fahd Jarad Humaira Kalsoom Yu-Ming Chu |
| author_facet | Shuang-Shuang Zhou Saima Rashid Fahd Jarad Humaira Kalsoom Yu-Ming Chu |
| author_sort | Shuang-Shuang Zhou |
| collection | DOAJ |
| description | Abstract In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators. |
| first_indexed | 2024-12-14T11:00:34Z |
| format | Article |
| id | doaj.art-9952239e9f9d4ac889f9293d279de5ef |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T11:00:34Z |
| publishDate | 2020-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-9952239e9f9d4ac889f9293d279de5ef2022-12-21T23:04:44ZengSpringerOpenAdvances in Difference Equations1687-18472020-06-012020111510.1186/s13662-020-02730-wNew estimates considering the generalized proportional Hadamard fractional integral operatorsShuang-Shuang Zhou0Saima Rashid1Fahd Jarad2Humaira Kalsoom3Yu-Ming Chu4School of Science, Hunan City UniversityDepartment of mathematics, Government UniversityDepartment of Mathematics, Çankaya UniversitySchool of Mathematical Sciences, Zhejiang UniversityDepartment of Mathematics, Huzhou UniversityAbstract In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators.http://link.springer.com/article/10.1186/s13662-020-02730-wGrüss inequalityFractional calculusGeneralized proportional Hadamard fractional integral operatorRiemann–Liouville fractional integral operator |
| spellingShingle | Shuang-Shuang Zhou Saima Rashid Fahd Jarad Humaira Kalsoom Yu-Ming Chu New estimates considering the generalized proportional Hadamard fractional integral operators Advances in Difference Equations Grüss inequality Fractional calculus Generalized proportional Hadamard fractional integral operator Riemann–Liouville fractional integral operator |
| title | New estimates considering the generalized proportional Hadamard fractional integral operators |
| title_full | New estimates considering the generalized proportional Hadamard fractional integral operators |
| title_fullStr | New estimates considering the generalized proportional Hadamard fractional integral operators |
| title_full_unstemmed | New estimates considering the generalized proportional Hadamard fractional integral operators |
| title_short | New estimates considering the generalized proportional Hadamard fractional integral operators |
| title_sort | new estimates considering the generalized proportional hadamard fractional integral operators |
| topic | Grüss inequality Fractional calculus Generalized proportional Hadamard fractional integral operator Riemann–Liouville fractional integral operator |
| url | http://link.springer.com/article/10.1186/s13662-020-02730-w |
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