New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator
Abstract Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03075-0 |
| _version_ | 1827381885893869568 |
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| author | İzzettin Demir Tuba Tunç |
| author_facet | İzzettin Demir Tuba Tunç |
| author_sort | İzzettin Demir |
| collection | DOAJ |
| description | Abstract Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite–Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems. |
| first_indexed | 2024-03-08T14:11:22Z |
| format | Article |
| id | doaj.art-94767a76a17d490683e6222a23cec92a |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-08T14:11:22Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-94767a76a17d490683e6222a23cec92a2024-01-14T12:42:20ZengSpringerOpenJournal of Inequalities and Applications1029-242X2024-01-012024111510.1186/s13660-023-03075-0New midpoint-type inequalities in the context of the proportional Caputo-hybrid operatorİzzettin Demir0Tuba Tunç1Department of Mathematics, Faculty of Science and Arts, Duzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityAbstract Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite–Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems.https://doi.org/10.1186/s13660-023-03075-0Hermite–Hadamard-type inequalitiesMidpoint-type inequalitiesConvex functionsProportional Caputo-hybrid operator |
| spellingShingle | İzzettin Demir Tuba Tunç New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator Journal of Inequalities and Applications Hermite–Hadamard-type inequalities Midpoint-type inequalities Convex functions Proportional Caputo-hybrid operator |
| title | New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator |
| title_full | New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator |
| title_fullStr | New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator |
| title_full_unstemmed | New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator |
| title_short | New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator |
| title_sort | new midpoint type inequalities in the context of the proportional caputo hybrid operator |
| topic | Hermite–Hadamard-type inequalities Midpoint-type inequalities Convex functions Proportional Caputo-hybrid operator |
| url | https://doi.org/10.1186/s13660-023-03075-0 |
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