Generalized AB-Fractional Operator Inclusions of Hermite-Hadamard's Type via Fractional Integration

被引：8

作者：

Bin-Mohsin, Bandar ^{[1
]}

Awan, Muhammad Uzair ^{[2
]}

Javed, Muhammad Zakria ^{[2
]}

Khan, Awais Gul ^{[2
]}

Budak, Huseyin ^{[3
]}

Mihai, Marcela V. ^{[4
]}

Noor, Muhammad Aslam ^{[5
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] Govt Coll Univ, Dept Math, Faisalabad 38000, Pakistan

[3] Duzce Univ, Fac Sci & Arts, Dept Math, TR-81620 Duzce, Turkiye

[4] Romanian Math Soc, Dept Sci Method Sess, Branch Bucharest, Acad St 14, RO-010014 Bucharest, Romania

[5] COMSATS Univ Islamabad, Dept Math, Islamabad 4000, Pakistan

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 05期

关键词：

Hermite-Hadamard inequality; pachpatte inequality; Mittag-Leffler; fractional integrals; preinvex function; Fejer; CONVEX-FUNCTIONS; INEQUALITIES;

D O I：

10.3390/sym15051012

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function E-mu,alpha,l(gamma,delta, k,c) (tau; p) as a kernel in the interval domain. Additionally, a new form of Atangana-Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in E-mu,alpha,l(gamma,delta, k,c)(tau; p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.

引用

页数：21

共 36 条

[1] On new fractional integral inequalities forp-convexity within interval-valued functions [J].