指数核分式积分的进一步赫米特-哈达马德式不等式

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2024-06-07 DOI:10.3390/fractalfract8060345

Hong Li, B. Meftah, Wedad Saleh, Hongyan Xu, A. Kiliçman, A. Lakhdari

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引用次数: 0

摘要

本文介绍了涉及具有指数核的分数积分算子的赫米特-哈达玛、中点和梯形不等式的新版本。我们探讨了可微凸函数的这些不等式，并证明了它们与经典积分的联系。本文通过一个具有图形表示的数值示例验证了推导出的不等式，并提供了一些实际应用，突出了它们与特殊手段的相关性。本研究提出了新的结果，除了我们研究的分数积分之外，当分数阶 β 接近 1 时，还对经典积分提出了新的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order β approaches 1, in addition to the fractional integrals we examined.

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.