In this paper, we aim at establishing an analog of the recently published results [1] with the help of new k-type fractional integral operator R ω [ f ](t) , which is introduced here by using the ω -weighted classes.Then we establish some new ω -weighted Pólya-Szegö type integral inequalities and ω -weighted fractional integral inequalities, which are the an analog of the recently published results [1].