In this paper, we have obtained new Hermite Hadamard Fejer type inequality different from the classical fejer inequality. With the help of this inequality, we have achieved Hermite Hadamard inequality for all of the Riemann Liouville and Conformable fractional integral that are both available and can be obtained.

In this work, the concepts of quantum derivative and quantum integral are renamed to be the left quantum derivative and the left de…nite quantum integral. Symmetrically to the left, a new quantum derivative (the right) and de…nite quantum integral (the right) are de…ned. Some properties of these new concepts are investigated and as well as according todo these new concepts some inaccuracies in quantum integral inequalities are corrected. Moreover, some new quantum Hermite-Hadamard type inequalities are established.