  Based on the concept and properties of $C^{*}$-algebras, the paper introduces
a concept of $C_{*}$-class functions. Then by using these functions in
$C^{*}$-algebra- valued modular metric spaces of moeini et al. [14], some
common fixed point theorems for self-mappings are established. Also, to support
of our results an application is provided for existence and uniqueness of
solution for a system of integral equations.
