Certain Grüss-type inequalities via tempered fractional integrals concerning another function

Journal of inequalities and applications

article

Gauhar Rahman¹  Kottakkaran Sooppy Nisar²  Saima Rashid³  Thabet Abdeljawad⁴ 

[1] Department of Mathematics, Shaheed Benazir Bhutto University;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University;Department of Mathematics, Government College University;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University

关键词: Fractional integrals;    Generalized tempered fractional integrals;    Inequalities;   

DOI  :  10.1186/s13660-020-02420-x

学科分类：电力

来源: SpringerOpen

【 摘 要 】

We study a generalized left sided tempered fractional (GTF)-integral concerning another function Ψ in the kernel. Then we investigate several kinds of inequalities such as Grüss-type and certain other related inequalities by utilizing the GTF-integral. Additionally, we present various special cases of the main result. By utilizing the connection between GTF-integral and Riemann–Liouville integral concerning another function Ψ in the kernel, certain distinct particular cases of the main result are also presented. Furthermore, certain other inequalities can be formed by applying various kinds of conditions on the function Ψ.

【 授权许可】

CC BY