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

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

引用次数: 0

Abstract

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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通过泰勒公式计算卡普托分数导数的维尔廷格型不等式

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。

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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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

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