On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator
Abstract In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportiona...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01852-4 |
| _version_ | 1797233499879505920 |
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| author | Tuba Tunç İzzettin Demir |
| author_facet | Tuba Tunç İzzettin Demir |
| author_sort | Tuba Tunç |
| collection | DOAJ |
| description | Abstract In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs. |
| first_indexed | 2024-04-24T16:17:09Z |
| format | Article |
| id | doaj.art-f9361e725eb9464cae79e33a4e60ef3b |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-24T16:17:09Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-f9361e725eb9464cae79e33a4e60ef3b2024-03-31T11:27:05ZengSpringerOpenBoundary Value Problems1687-27702024-03-012024111710.1186/s13661-024-01852-4On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operatorTuba Tunç0İzzettin Demir1Department of Mathematics, Faculty of Science and Arts, Duzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityAbstract In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs.https://doi.org/10.1186/s13661-024-01852-4Hermite–Hadamard-type inequalitiesMidpoint-type inequalitiesConvex functionsRiemann–Liouville fractional integralsProportional Caputo-hybrid operator |
| spellingShingle | Tuba Tunç İzzettin Demir On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator Boundary Value Problems Hermite–Hadamard-type inequalities Midpoint-type inequalities Convex functions Riemann–Liouville fractional integrals Proportional Caputo-hybrid operator |
| title | On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator |
| title_full | On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator |
| title_fullStr | On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator |
| title_full_unstemmed | On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator |
| title_short | On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator |
| title_sort | on a new version of hermite hadamard type inequality based on proportional caputo hybrid operator |
| topic | Hermite–Hadamard-type inequalities Midpoint-type inequalities Convex functions Riemann–Liouville fractional integrals Proportional Caputo-hybrid operator |
| url | https://doi.org/10.1186/s13661-024-01852-4 |
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