Some new Grüss inequalities associated with generalized fractional derivative

AIMS Mathematics

article

Sajid Iqbal¹  Muhammad Samraiz²  Gauhar Rahman³  Kottakkaran Sooppy Nisar⁴  Thabet Abdeljawad⁵ 

[1] Department of Mathematics & Statistics, Institute of Southern Punjab;Department of Mathematics, University of Sargodha;Department of Mathematics and Statistics, Hazara University;Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University;Department of Mathematics and Sciences, Prince Sultan University;Department of Medical Research, China Medical University

关键词: Grüss-type inequalities;    kernel;    fractional derivative;    Young's inequality;   

DOI  :  10.3934/math.2023010

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we prove several new integral inequalities for the $ k $-Hilfer fractional derivative operator, which is a fractional calculus operator. As a result, we have a whole new set of fractional integral inequalities. For the generalized fractional derivative, we also use Young's inequality to find new forms of inequalities. Such conclusions for this novel and generalized fractional derivative are extremely useful and valuable in the domains of differential equations and fractional differential calculus, both of which have a strong connections to real-world situations. These findings may stimulate additional research in a variety of fields of pure and applied sciences.

【 授权许可】

CC BY