The Grüss-Type and Some Other Related Inequalities via Fractional Integral with Respect to Multivariate Mittag-Leffler Function

Abstract

In the recent era of research, the field of integral inequalities has earned more recognition due to its wide applications in diverse domains. The researchers have widely studied the integral inequalities by utilizing different approaches. In this present article, we aim to develop a variety of certain new inequalities using the generalized fractional integral in the sense of multivariate Mittag-Leffler (M-L) functions, including Grüss-type and some other related inequalities. Also, we use the relationship between the Riemann-Liouville integral, the Prabhakar integral, and the generalized fractional integral to deduce specific findings. Moreover, we support our findings by presenting examples and corollaries.

Keywords

• fractional integrals
• generalized fractional integrals
• Prabhakar integral
• Mittag-Leffler function
• inequalities