Generalized proportional fractional integral functional bounds in Minkowski’s inequalities
Abstract In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ. The functions used in this work are bounded by two positive functions...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03582-8 |
| _version_ | 1831672803074506752 |
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| author | Tariq A. Aljaaidi Deepak B. Pachpatte Wasfi Shatanawi Mohammed S. Abdo Kamaleldin Abodayeh |
| author_facet | Tariq A. Aljaaidi Deepak B. Pachpatte Wasfi Shatanawi Mohammed S. Abdo Kamaleldin Abodayeh |
| author_sort | Tariq A. Aljaaidi |
| collection | DOAJ |
| description | Abstract In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ. The functions used in this work are bounded by two positive functions to get reverse Minkowski inequalities in a new sense. Moreover, we introduce new fractional integral inequalities which have a close relationship to the reverse Minkowski-type inequalities via ψ-proportional fractional integral, then with the help of this fractional integral operator, we discuss some new special cases of reverse Minkowski-type inequalities through this work. An open issue is covered in the conclusion section to extend the current findings to be more general. |
| first_indexed | 2024-12-19T23:58:19Z |
| format | Article |
| id | doaj.art-b4d95fca825e43a9ba8cd818f3ee2c35 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T23:58:19Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-b4d95fca825e43a9ba8cd818f3ee2c352022-12-21T20:00:55ZengSpringerOpenAdvances in Difference Equations1687-18472021-09-012021111710.1186/s13662-021-03582-8Generalized proportional fractional integral functional bounds in Minkowski’s inequalitiesTariq A. Aljaaidi0Deepak B. Pachpatte1Wasfi Shatanawi2Mohammed S. Abdo3Kamaleldin Abodayeh4Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada UniversityDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada UniversityDepartment of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, Hodeidah UniversityDepartment of Mathematics and General Sciences, Prince Sultan UniversityAbstract In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ. The functions used in this work are bounded by two positive functions to get reverse Minkowski inequalities in a new sense. Moreover, we introduce new fractional integral inequalities which have a close relationship to the reverse Minkowski-type inequalities via ψ-proportional fractional integral, then with the help of this fractional integral operator, we discuss some new special cases of reverse Minkowski-type inequalities through this work. An open issue is covered in the conclusion section to extend the current findings to be more general.https://doi.org/10.1186/s13662-021-03582-8Minkowski inequalitiesFractional inequalitiesψ-proportional fractional operators |
| spellingShingle | Tariq A. Aljaaidi Deepak B. Pachpatte Wasfi Shatanawi Mohammed S. Abdo Kamaleldin Abodayeh Generalized proportional fractional integral functional bounds in Minkowski’s inequalities Advances in Difference Equations Minkowski inequalities Fractional inequalities ψ-proportional fractional operators |
| title | Generalized proportional fractional integral functional bounds in Minkowski’s inequalities |
| title_full | Generalized proportional fractional integral functional bounds in Minkowski’s inequalities |
| title_fullStr | Generalized proportional fractional integral functional bounds in Minkowski’s inequalities |
| title_full_unstemmed | Generalized proportional fractional integral functional bounds in Minkowski’s inequalities |
| title_short | Generalized proportional fractional integral functional bounds in Minkowski’s inequalities |
| title_sort | generalized proportional fractional integral functional bounds in minkowski s inequalities |
| topic | Minkowski inequalities Fractional inequalities ψ-proportional fractional operators |
| url | https://doi.org/10.1186/s13662-021-03582-8 |
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