On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions
The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in th...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8829140 |
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| _version_ | 1832546782131781632 |
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| author | Xiaobin Wang Muhammad Shoaib Saleem Kiran Naseem Aslam Xingxing Wu Tong Zhou |
| author_facet | Xiaobin Wang Muhammad Shoaib Saleem Kiran Naseem Aslam Xingxing Wu Tong Zhou |
| author_sort | Xiaobin Wang |
| collection | DOAJ |
| description | The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h-convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers. |
| format | Article |
| id | doaj-art-08d8b160b915451cb606156c438d7312 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-08d8b160b915451cb606156c438d73122025-02-03T06:46:58ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88291408829140On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex FunctionsXiaobin Wang0Muhammad Shoaib Saleem1Kiran Naseem Aslam2Xingxing Wu3Tong Zhou4College of Science, Xinjiang Institute of Technology, Aksu 843100, ChinaDepartment of Mathematics, University of Okara, Okara, PakistanDepartment of Mathematics, University of Okara, Okara, PakistanCollege of Science, Xinjiang Institute of Technology, Aksu 843100, ChinaPublic Basic Teaching Department, Xinjiang Institute of Technology, Aksu 843100, ChinaThe theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h-convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers.http://dx.doi.org/10.1155/2020/8829140 |
| spellingShingle | Xiaobin Wang Muhammad Shoaib Saleem Kiran Naseem Aslam Xingxing Wu Tong Zhou On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions Journal of Mathematics |
| title | On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions |
| title_full | On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions |
| title_fullStr | On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions |
| title_full_unstemmed | On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions |
| title_short | On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions |
| title_sort | on caputo fabrizio fractional integral inequalities of hermite hadamard type for modified h convex functions |
| url | http://dx.doi.org/10.1155/2020/8829140 |
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