Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function

Abstract

In this paper, by adopting the classical method of proofs, we establish certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. The main results are more general and include a large number of available classical fractional integral inequalities in the literature. Furthermore, some new fractional integral inequalities similar to the main results can be also obtained by employing the newly introduced generalized fractional integral operators involving the Mittag-Leffler-like function and weighted function. Consequently, their relevance with known inequalities for different kinds of fractional integral operators are pointed out.

Certain New Reverse Hölder- and Minkowski-Type Inequalities for Modified Unified Generalized Fractional Integral Operators with Extended Unified Mittag–Leffler Functions

“…In 2022, taking advantage of the MLLF, the author [34,35] introduced the following generalized FIOs. Definition 7 ([34,35]).…”

Discrete Local Fractional Hilbert-type Inequalities

“…Over the last ten years, by using the kinds of generalized fractional integral operators, a great deal of fractional integral inequalities have been presented [2][3][4][5]. Recently, local fractional calculus has caused widespread attention from many scholars, we give basic definitions and results of the local fractional calculus (see [6][7][8][9][10][11][12][13]).…”