A functional differential equation is a differential equation with deviating argument. That is, a functional differential equation is an equation that contains a function and some of its derivatives evaluated at different argument values.[1]
Functional differential equations find use in mathematical models that assume a specified behavior or phenomenon depends on the present as well as the past state of a system.[2] In other words, past events explicitly influence future results. For this reason, functional differential equations are more applicable than ordinary differential equations (ODE), in which future behavior only implicitly depends on the past.