The paper aimed to achieve three primary objectives. First, it introduced significant common fixed point results in the context of newly proposed partial modular $b-$metric spaces, thus contributing to the advancement of this field. Second, it presented unique results using a direct approach that did not depend on the strong continuity of the mapping, thereby offering a valuable perspective. Finally, it applied previously established convergence techniques to determine a common solution for a system of Fredholm integral equations, demonstrating the practical implications of the theoretical findings.