Some generalizations of dynamic Opial-type inequalities in conformable calculus
Abstract In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and exten...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-11-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-024-03224-z |
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| author | Fatma M. Khamis M. M. A. El-Sheikh Thabet Abdeljawad Aiman Mukheimer Gamal A. F. Ismail |
| author_facet | Fatma M. Khamis M. M. A. El-Sheikh Thabet Abdeljawad Aiman Mukheimer Gamal A. F. Ismail |
| author_sort | Fatma M. Khamis |
| collection | DOAJ |
| description | Abstract In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α = 1 $\alpha = 1$ , our results cover some well-known inequalities of Opial-type on time scales. |
| format | Article |
| id | doaj-art-f2ae07c7891143b0a6c35a06117dfd18 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-f2ae07c7891143b0a6c35a06117dfd182024-12-01T12:50:07ZengSpringerOpenJournal of Inequalities and Applications1029-242X2024-11-012024111510.1186/s13660-024-03224-zSome generalizations of dynamic Opial-type inequalities in conformable calculusFatma M. Khamis0M. M. A. El-Sheikh1Thabet Abdeljawad2Aiman Mukheimer3Gamal A. F. Ismail4Faculty of Women for (Art, Science, and Education), Department of Mathematics, Ain Shams UniversityDepartment of Mathematics and Computer Science, Faculty of Science, Menoufia UniversityDepartment of Mathematics and Science, Prince Sultan UniversityDepartment of Mathematics and Science, Prince Sultan UniversityFaculty of Women for (Art, Science, and Education), Department of Mathematics, Ain Shams UniversityAbstract In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α = 1 $\alpha = 1$ , our results cover some well-known inequalities of Opial-type on time scales.https://doi.org/10.1186/s13660-024-03224-zOpial-type inequalityDynamic inequalityHölder inequalityConformable fractional calculus |
| spellingShingle | Fatma M. Khamis M. M. A. El-Sheikh Thabet Abdeljawad Aiman Mukheimer Gamal A. F. Ismail Some generalizations of dynamic Opial-type inequalities in conformable calculus Journal of Inequalities and Applications Opial-type inequality Dynamic inequality Hölder inequality Conformable fractional calculus |
| title | Some generalizations of dynamic Opial-type inequalities in conformable calculus |
| title_full | Some generalizations of dynamic Opial-type inequalities in conformable calculus |
| title_fullStr | Some generalizations of dynamic Opial-type inequalities in conformable calculus |
| title_full_unstemmed | Some generalizations of dynamic Opial-type inequalities in conformable calculus |
| title_short | Some generalizations of dynamic Opial-type inequalities in conformable calculus |
| title_sort | some generalizations of dynamic opial type inequalities in conformable calculus |
| topic | Opial-type inequality Dynamic inequality Hölder inequality Conformable fractional calculus |
| url | https://doi.org/10.1186/s13660-024-03224-z |
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