Hermite-Hadamard Fractional Inequalities for Differentiable Functions

被引：7

作者：

Samraiz, Muhammad ^{[1
]}

Perveen, Zahida ^{[1
]}

Rahman, Gauhar ^{[2
]}

Khan, Muhammad Adil ^{[3
]}

Nisar, Kottakkaran Sooppy ^{[4
]}

机构：

[1] Univ Sargodha, Dept Math, Sargodha 40100, Pakistan

[2] Hazara Univ, Dept Math & Stat, Mansehra 21300, Pakistan

[3] Univ Peshawar, Dept Math, Peshawar 25000, Pakistan

[4] Prince Sattam Bin Abdulaziz Univ, Dept Math, Coll Arts & Sci, Wadi Aldawser 11991, Saudi Arabia

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 02期

关键词：

Hermite-Hadamard-type inequalities; Hilfer fractional derivative; Holder's inequality; 26D15; 26D07; 26D10; 26A33; 26A51;

D O I：

10.3390/fractalfract6020060

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we look at a variety of mean-type integral inequalities for a well-known Hilfer fractional derivative. We consider twice differentiable convex and s-convex functions for <mml:semantics>s is an element of (0,1]</mml:semantics> that have applications in optimization theory. In order to infer more interesting mean inequalities, some identities are also established. The consequences for Caputo fractional derivative are presented as special cases to our general conclusions.

引用

页数：17

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