The aim of this manuscript is to prove some fixed point results for α_*-admissible mapping with a new approach of (α_*,ψ_(S_b ) )-contraction in complete S_b-metric space. As a work that extends and enhances the existing investigation of α_*- admissible mappings with regard to ψ. finally, in order to demonstrate the relevance of our ideas and to bolster our findings, we also provide an application to the Fredholm integral equation and the existing solution of functional equations