Generalizations of Hermite–Hadamard like inequalities involving \(\chi _{{\kappa }}\) -Hilfer fractional integrals

Advances in Difference Equations

article

Chu, Yu-Ming¹  Awan, Muhammad Uzair²  Talib, Sadia²  Noor, Muhammad Aslam³  Noor, Khalida Inayat³ 

[1] Department of Mathematics, Huzhou University;Department of Mathematics, Government College University;Department of Mathematics, COMSATS University Islamabad

关键词: Convex;    s -convex;    Fractional;    Hilfer;    Hermite–Hadamard inequality;   

DOI  :  10.1186/s13662-020-03059-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The main objective of this paper is to obtain a new κ-fractional analogue of Hermite–Hadamard’s inequality using the class of s-convex functions and$\chi _{{\kappa }}$ -Hilfer fractional integrals. In order to obtain other main results of the paper we derive two new fractional integral identities using the definitions of$\chi _{{\kappa }}$ -Hilfer fractional integrals. For the validity of these identities we also take some particular examples. Using these identities we then obtain some more new variants of Hermite–Hadamard’s inequality using s-convex functions.

【 授权许可】

CC BY