In this paper, we establish the Hermite-Hadamard type inequalities forconformable fractional integral and we will investigate some integralinequalities connected with the left and right-hand side of theHermite-Hadamard type inequalities for conformable fractional integral. Theresults presented here would provide generalizations of those given inearlier works and we show that some of our results are better than the otherresults with respect to midpoint inequalities.

Some generalized integral inequalities are established for the fractional expectation and the fractional variance for continuous random variables. Special cases of integral inequalities in this paper are studied by Barnett et al. and Dahmani.

In this study, giving the definition of fractional integral, which are with the help of synchronous and monotonic function, some fractional integral inequalities have established.

In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of two variables via quantum integrals. We also consider the particular cases of the key results and offer some new integral inequalities.

In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣ D q 2 b f ∣ | {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣ D q 2 a f ∣ | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving q a {q}_{a} and q b {q}^{b} -quantum integrals. The results presented here are the generalization of already published ones.