On nabla conformable fractional Hardy-type inequalities on arbitrary time scales
Abstract The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the lit...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02723-7 |
| _version_ | 1818337575345061888 |
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| author | Ahmed A. El-Deeb Samer D. Makharesh Eze R. Nwaeze Olaniyi S. Iyiola Dumitru Baleanu |
| author_facet | Ahmed A. El-Deeb Samer D. Makharesh Eze R. Nwaeze Olaniyi S. Iyiola Dumitru Baleanu |
| author_sort | Ahmed A. El-Deeb |
| collection | DOAJ |
| description | Abstract The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed. |
| first_indexed | 2024-12-13T14:57:24Z |
| format | Article |
| id | doaj.art-5b06c9c16b5c4b7ea85a4d87b15d17d4 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T14:57:24Z |
| publishDate | 2021-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-5b06c9c16b5c4b7ea85a4d87b15d17d42022-12-21T23:41:12ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-12-012021112310.1186/s13660-021-02723-7On nabla conformable fractional Hardy-type inequalities on arbitrary time scalesAhmed A. El-Deeb0Samer D. Makharesh1Eze R. Nwaeze2Olaniyi S. Iyiola3Dumitru Baleanu4Department of Mathematics, Faculty of Science, Al-Azhar UniversityDepartment of Mathematics, Faculty of Science, Al-Azhar UniversityDepartment of Mathematics and Computer Science, Alabama State UniversityDepartment of Mathematics, Clarkson UniversityDepartment of Mathematics, Cankaya UniversityAbstract The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.https://doi.org/10.1186/s13660-021-02723-7Fractional calculusCalculus on time scalesConformable nabla derivativeConformable nabla integralHardy’s inequality |
| spellingShingle | Ahmed A. El-Deeb Samer D. Makharesh Eze R. Nwaeze Olaniyi S. Iyiola Dumitru Baleanu On nabla conformable fractional Hardy-type inequalities on arbitrary time scales Journal of Inequalities and Applications Fractional calculus Calculus on time scales Conformable nabla derivative Conformable nabla integral Hardy’s inequality |
| title | On nabla conformable fractional Hardy-type inequalities on arbitrary time scales |
| title_full | On nabla conformable fractional Hardy-type inequalities on arbitrary time scales |
| title_fullStr | On nabla conformable fractional Hardy-type inequalities on arbitrary time scales |
| title_full_unstemmed | On nabla conformable fractional Hardy-type inequalities on arbitrary time scales |
| title_short | On nabla conformable fractional Hardy-type inequalities on arbitrary time scales |
| title_sort | on nabla conformable fractional hardy type inequalities on arbitrary time scales |
| topic | Fractional calculus Calculus on time scales Conformable nabla derivative Conformable nabla integral Hardy’s inequality |
| url | https://doi.org/10.1186/s13660-021-02723-7 |
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