On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications
The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6625597 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850167331006709760 |
|---|---|
| author | Qi Li Muhammad Shoaib Saleem Peiyu Yan Muhammad Sajid Zahoor Muhammad Imran |
| author_facet | Qi Li Muhammad Shoaib Saleem Peiyu Yan Muhammad Sajid Zahoor Muhammad Imran |
| author_sort | Qi Li |
| collection | DOAJ |
| description | The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly convex functions involving the Caputo–Fabrizio fractional integral operator are also presented. Moreover, we present some applications of the proposed inequalities to special means. |
| format | Article |
| id | doaj-art-e22f7f04c6ef4d3c9064242bb765ae02 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e22f7f04c6ef4d3c9064242bb765ae022025-08-20T02:21:13ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66255976625597On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some ApplicationsQi Li0Muhammad Shoaib Saleem1Peiyu Yan2Muhammad Sajid Zahoor3Muhammad Imran4Basic Teaching Department, Shandong Huayu University of Technology, Dezhou 253034, Shandong, ChinaDepartment of Mathematics, University of Okara, Okara, PakistanBasic Teaching Department, Shandong Huayu University of Technology, Dezhou 253034, Shandong, ChinaDepartment of Mathematics, University of Okara, Okara, PakistanDepartment of Mathematics, University of Okara, Okara, PakistanThe theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly convex functions involving the Caputo–Fabrizio fractional integral operator are also presented. Moreover, we present some applications of the proposed inequalities to special means.http://dx.doi.org/10.1155/2021/6625597 |
| spellingShingle | Qi Li Muhammad Shoaib Saleem Peiyu Yan Muhammad Sajid Zahoor Muhammad Imran On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications Journal of Mathematics |
| title | On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications |
| title_full | On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications |
| title_fullStr | On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications |
| title_full_unstemmed | On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications |
| title_short | On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications |
| title_sort | on strongly convex functions via caputo fabrizio type fractional integral and some applications |
| url | http://dx.doi.org/10.1155/2021/6625597 |
| work_keys_str_mv | AT qili onstronglyconvexfunctionsviacaputofabriziotypefractionalintegralandsomeapplications AT muhammadshoaibsaleem onstronglyconvexfunctionsviacaputofabriziotypefractionalintegralandsomeapplications AT peiyuyan onstronglyconvexfunctionsviacaputofabriziotypefractionalintegralandsomeapplications AT muhammadsajidzahoor onstronglyconvexfunctionsviacaputofabriziotypefractionalintegralandsomeapplications AT muhammadimran onstronglyconvexfunctionsviacaputofabriziotypefractionalintegralandsomeapplications |