Integral operators with the Mittag–Leffler function in kernels play a very vital role generalizing classical integral inequalities. This paper aims to derive Ostrowski-type inequalities for k-fractional integrals containing functions. Several new can be deduced various fractional particular cases. Applications of these are also given.

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

We study weak-type (1, 1) weighted inequalities for the fractional integral operator Iα. We show that the fractional maximal operatorMα controls these inequalities when the weight is radially decreasing. However, we exhibit some counterexamples which show that Mα is not appropriate for this control on general weights. We do provide, nevertheless, some positive results related to this problem by...

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

Multiplicative calculus, also called non-Newtonian represents an alternative approach to the usual calculus of Newton (1643–1727) and Leibniz (1646–1716). This type was first introduced by Grossman Katz it provides a defined calculation, from start, for positive real numbers only. In this investigation, we propose study symmetrical fractional multiplicative inequalities Simpson type. For this, ...

In this paper, we obtained some new estimates on generalization of Hadamard, Ostrowski and Simpson-like type inequalities for harmonically quasi-convex functions via Riemann Liouville fractional integral.