Common solution to a coupled system of fractional differential equations and nonlinear integral equations via weakly altering distance functions and $w$-distance

The current study addresses here to demonstrate that the a common solution to a system of nonlinear fractional differential equations and Fredholm-Volterra integral equations exists and is unique with their employing common fixed point outcomes and examples to illustrate the concept. A number of typical fixed point results that satisfy the generalized contraction principle are demonstrated via weak altering distance and $w$-distance functions. Following that, numerical experiments and an example are presented to validate the usefulness of our result.