Generalized k-Fractional Chebyshev-Type Inequalities via Mittag-Leffler Functions

Abstract

Mathematical inequalities have gained importance and popularity due to the application of integral operators of different types. The present paper aims to give Chebyshev-type inequalities for generalized k-integral operators involving the Mittag-Leffler function in kernels. Several new results can be deduced for different integral operators, along with Riemann–Liouville fractional integrals by substituting convenient parameters. Moreover, the presented results generalize several already published inequalities.

Grüss Type k-Fractional Integral Operator Inequalities and Allied Results

“…Recently, in [30], Zhang et al introduced the generalized k-integral operators involving Mittag-Leffler function as follows:…”

Chebyshev-Type Inequalities Involving ( k , ψ )-Proportional Fractional Integral Operators

“…In [32], authors used the generalized Katugampola operators to establish integral inequalities for Chebyshev and extended Chebyshev functionals. In the literature, a number of mathematicians have devoted their efforts to study Chebyshev-type inequalities using various fractional operators [33][34][35][36][37][38].…”

Inequalities of the Ostrowski Type Associated with Fractional Integral Operators Containing the Mittag–Leffler Function

“…Zhang et al [21] introduced the generalized k-fractional integrals involving the Mittag-Leffler function as follows:…”

“…Remark 1. From fractional integrals (6) and (7), various new fractional integrals containing the Mittag-Leffler function can be deduced (for details, see [21], Remark 1). Further, the fractional integrals (6) and (7) reproduce many already-defined fractional integrals (for details, see [21], Remark 2).…”

“…Then, by applying this identity and k-fractional integrals (6) and (7), Ostrowski-type inequalities are established. It is mentioned that several new Ostrowski-type inequalities can be deduced for the well-known fractional integrals compiled in [21] (Remarks 1 and 2). In the last section, some applications of the presented results are given.…”