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May 27, 2026Filomat0 citationsOpen Access

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

Key Points

The research aims to explore new inequalities involving modified unified generalized fractional integral operators and extended unified Mittag-Leffler functions.
Investigated inequalities involving MUGFIOs for positive continuous monotonic and convex functions.
Established Chebyshev and reversed Minkowski inequalities for these operators.
Developed a framework that extends classical inequality results.
Novel MUGFIO inequalities were established for positive continuous monotonic and convex functions.
New Chebyshev and reversed Minkowski inequalities were introduced using MUGFIOs with EUMLFs.

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.

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