In this work, we first establish new Hermite-Hadamard inequalities for convex function utilizing fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover , we obtain some generalized midpoint and trapezoid type inequalities for these kinds of fractional integrals. The inequalities given in this paper provide generalizations of several results obtained in earlier works