Grüss-type inequalities involving functional bounds via analytic kernel fractional integral

The main objective of this paper is to obtain a generalization of some Grüss-type inequalities in the case of functional bounds by using a generalized analytical kernel Riemann-Liouville fractional integral. The study leverages analytic kernel functions and tools like Young's Inequality and Cauchy-Schwarz Inequality to ensure rigorous bounds. Limitations include computational complexity and restrictions to real parameters. We have developed and presented the Grüss-type inequality in a more general way, enabling mathematicians to utilize it more effectively through the generalized fractional integral involving an analytic kernel operator. The work opens avenues for future research in complex fractional calculus and practical applications.•We have used the recently generalized fractional integral operator to present Grüss-type inequalities in the case of functional bounds of a single order.•We investigated a generalization of some Grüss-type inequalities in the case of functional bounds of distinct orders by using the generalized fractional integral.•We discussed several exceptional cases and presented the corresponding results.