通过泰勒公式计算卡普托分数导数的维尔廷格型不等式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-04 DOI:10.1186/s13660-024-03194-2

Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık

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引用次数: 0

摘要

在本研究中，我们首先推导出一个 Wirtinger 型结果，借助左侧和右侧分式泰勒公式，给出了函数平方积分与其卡普托分式导数平方积分之间的联系。随后，我们通过荷尔德不等式，给出了涉及 $L_{r}$ norm 的 $r>1$ 的卡普托分数导数的更一般的不等式。此外，我们还通过卡普托分数导数与黎曼-黎奥维尔分数导数之间的关系，提出了黎曼-黎奥维尔分数导数的类似不等式。

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Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional Taylor’s Formulas. Afterward, we provide a more general inequality involving Caputo fractional derivatives for $L_{r}$ norm with $r>1$ via Hölder’s inequality. Also, similar inequalities for Riemann–Liouville fractional derivatives are presented by means of a relation between Caputo fractional derivatives and Riemann–Liouville fractional derivatives.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.