Our paper is ardent to prove fixed point theorems in the axioms of ????− multiplicative metric spaces for rational type contraction conditions. The presented theorem extends the research results of Merdaci Seddik1 and Hamaizia Taieb [6] and broadens a number of well-known findings in the setting of b-multiplicative metric spaces. Subsequently, we use our main results to find out the proximate solution of the Fredholm integral equation.