On The (k,s)-Hilfer Fractional Derivatives via Wirtinger-Type Inequalities and Their Analytical Applications

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2026-04-13 DOI:10.1002/malq.70020

Muhammad Samraiz, Areej Yussouf, Saima Naheed

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引用次数: 0

Abstract

This article introduces a novel definition of $(k, s)$ -Hilfer fractional derivative. Based on this derivative, some fractional Wirtinger type inequalities are established for the $L_{p}$ spaces, where $p > 1$ by using Hölder's inequality. Various related special cases are also presented. To validate our main results, examples with graphical representations are provided. Applications of $(k, s)$ -Hilfer fractional Wirtinger-type inequalities are demonstrated in terms of arithmetic mean and geometric mean-type inequality.

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（k,s）-Hilfer分数阶导数的wirtingger型不等式及其解析应用

给出了（k,s）$ (k,s)$ -Hilfer分数阶导数的一个新定义。在此导数的基础上，利用Hölder的不等式，对p >； 1$ p > 1$的L p $L_{p}$空间建立了若干分数Wirtinger型不等式。还介绍了各种相关的特殊情况。为了验证我们的主要结果，提供了带有图形表示的示例。从算术平均数和几何平均数不等式的角度证明了（k,s）$ (k,s)$ -Hilfer分数wirtinger型不等式的应用。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.