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 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications 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

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.