  In this paper, the notion of $\mathbb{C}$-simulation function is introduced
and the existence and uniqueness of common fixed points of two self-mappings
satisfying contractive conditions in the setting of complex valued metric
spaces via $\mathbb{C}$-simulation functions are studied. Examples are also
provided to demonstrate the results. The existence and uniqueness of a
first-order periodic differential equation is also obtained as an application
of the result.
