Certain New Weighted Young- And Pólya–szegö-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function With Applications

Abstract

This paper investigates certain new weighted Young- and Pólya–Szegö-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. A large quantity of usable classical inequalities in the literature are included in the main results of this paper. Meanwhile, two types of new generalized weighted fractional integral operators are introduced to establish some new weighted Young- and Pólya–Szegö-type inequalities. As applications, several estimates of Chebyshev-type weighted unified fractional integral inequalities with two unknown functions are obtained by employing the Heaviside unit step function. Finally, some relations between main results and known inequalities for different kinds of fractional integral operators are provided.

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]).…”