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.

On the Generalization of Ostrowski-Type Integral Inequalities via Fractional Integral Operators with Application to Error Bounds

“…The inequalities ( 22) and (26) give the desired inequality (18). Similarly, the inequalities ( 23) and ( 27) give inequality (19).…”

“…In last few decades, various types of fractional integrals have been developed by using Mittag-Leffler functions in the kernel [13][14][15][16]. Several inequalities for different fractional integrals comprising the Mittag-Leffler function have been established by researchers [17][18][19].…”