Certain novel inequalities for monotonic and convex functions involving modified unified generalized fractional integral operators with extended unified Mittag-Leffler functions and related results

Abstract

In this study, based on the modified unified generalized fractional integral operators (MUGFIOs) with extended unified Mittag--Leffler functions (EUMLFs), we investigate certain new MUGFIO inequalities for some positive continuous monotonic functions and convex functions. Furthermore, some novel Chebyshev type inequalities and reversed Minkowski inequalities for MUGFIOs with EUMLFs are established. The presented results constitute a significant extension of classical inequalities in the literature, unifying and generalizing multiple existing frameworks through the proposed MUGFIOs with EUMLFs.