The aim of this paper is to establish the existence and uniqueness of the common solution for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations using the common fixed point results equipped with illustrative examples. Some common fixed point results satisfying the generalized contraction condition involving $w$-distance and weak altering distance functions are proved. Then, an example is provided to support the usability of our result along with numerical experiments.