The Minkowski inequality involving generalized k-fractional conformable integral

Abstract

In the research paper, the authors exploit the definition of a new class of fractional integral operators, recently proposed by Jarad et al. (Adv. Differ. Equ. 2017:247, 2017), to define a new class of generalized k-fractional integral operators and develop a generalization of the reverse Minkowski inequality involving the newly introduced fractional integral operators. The two new theorems correlating with this inequality, including statements and verifications of other inequalities via the suggested k-fractional conformable integral operators, are presented.

The Minkowski inequalities via generalized proportional fractional integral operators

“…In [10,45], the authors established the reverse Minkowski inequality for Hadamard fractional integral operators. In [31], Mubeen et al recently established the reverse Minkowski inequalities and some related inequalities for generalized k-fractional conformable integrals.…”

Certain Hadamard Proportional Fractional Integral Inequalities

“…Multiplying (21) by F (θ, ρ) (where F (θ, ρ) is defined in (16)) and integrating the resultant estimates with respect to ρ over (1, θ), we get…”

“…In [20], Huang et al investigated Hermite-Hadamard type inequalities for k-fractional conformable integrals. Mubeen et al [21] proposed the Minkowski's inequalities involving the generalized k-fractional conformable integrals. The chebyshev type inequalities involving generalized k-fractional conformable integrals can be found in the work of Qi et al [22].…”

Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

“…In [35], Aldhaifallah et al introduced some integral inequalities for a certain family of n(n ∈ N) positive continuous and decreasing functions on some intervals employing what is called generalized (k, s)-fractional integral operators. Recently, some researchers introduced a verity of certain interesting inequalities, applications, and properties for the conformable integrals [36][37][38][39][40].…”