This paper introduces coupled fixed points of maps in MIFSMS. The notion
of compatible maps and weakly compatible maps is also defined. Common
coupled fixed point theorem for weakly compatible maps have been proved
in the setting of MIFSMS. Moreover, some corollaries and an example is
given to validate our new result. Also, to show the usability of our
findings, we have applied our new result to get the solution of
nonlinear Fredholm integral equation.