On Grüss inequalities within generalized K-fractional integrals
Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Khalida Inayat Noor, Dumitru Bǎleanu, Jia‐Bao Liu
Abstract
Abstract In this paper, we introduce the generalized $\mathcal{K}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> -fractional integral in the frame of a new parameter $\mathcal{K}>0$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:math> . This paper offers some new important inequalities of Grüss type using the generalized $\mathcal{K}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> -fractional integral and associated integral inequalities. Our results with this new integral operator have the abilities to be implemented for the evaluation of many mathematical problems related to the real world applications.