Some new inequalities for (k,s)-fractional integrals

Abstract

In this paper, the (k, s)-fractional integral operator is used to generate new classes of integral inequalities using a family of n positive functions, (n ∈ N). Two classes of integral inequalities involving the (k, s)-fractional integral operator are derived here and these results allow us in particular to generalize some classical inequalities. Certain interesting consequent results of the main theorems are also pointed out.

Minkowski’s inequality for the AB-fractional integral operator

“…For instance, recently, Agarwal et al [6] proved Hermite-Hadamard-type inequalities by using generalized k-fractional-integrals. Aldhaifallah et al [7] used the (k, s)-fractional integral operator to generalize the inequalities for a family/class of n positive functions. Set et al [8] studied Hermite-Hadamard-type inequalities for a generalized fractional integral operator for functions with convex absolute values of derivatives.…”

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

“…Dahmani [34] presented a variety of integral inequalities by using some families of n positive functions. 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].…”

Certain inequalities via generalized proportional Hadamard fractional integral operators

“…In [10], the authors established fractional integral inequalities for a class of family of n (n ∈ N) positive continuous and decreasing functions on [a, b] by employing the (k, s)fractional integral operators. Recently, the fractional conformable integrals have attracted the attention of many researchers.…”