{"title":"雷纳分式算子的哈达玛德积分不等式的新估算方法","authors":"Merve Coşkun, Çetin Yıldız, Luminița-Ioana Cotîrlă","doi":"10.3390/fractalfract8050302","DOIUrl":null,"url":null,"abstract":"In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s=1, λ=α, σ(0)=1, and w=0. In conclusion, the methodology described in this article is expected to stimulate further research in this area.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"26 13","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Novel Estimations of Hadamard-Type Integral Inequalities for Raina’s Fractional Operators\",\"authors\":\"Merve Coşkun, Çetin Yıldız, Luminița-Ioana Cotîrlă\",\"doi\":\"10.3390/fractalfract8050302\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s=1, λ=α, σ(0)=1, and w=0. In conclusion, the methodology described in this article is expected to stimulate further research in this area.\",\"PeriodicalId\":510138,\"journal\":{\"name\":\"Fractal and Fractional\",\"volume\":\"26 13\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractal and Fractional\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/fractalfract8050302\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractal and Fractional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/fractalfract8050302","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们利用一类广泛的分数积分算子(即 Raina 分数算子),建立了赫尔墨特-哈达玛德类型的新型分数积分不等式。在著名的黎曼-刘维尔分数算子的帮助下,我们利用重要结果推导出了 s 型凸函数。我们还注意到,本研究的某些结论比在某些特定条件下(如 s=1、λ=α、σ(0)=1 和 w=0)得出的结论更为合理。
Novel Estimations of Hadamard-Type Integral Inequalities for Raina’s Fractional Operators
In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s=1, λ=α, σ(0)=1, and w=0. In conclusion, the methodology described in this article is expected to stimulate further research in this area.