Functional Differential Equations

Functional Differential Equations (FDEs) are equations where the rate of change of a function depends not only on its current state but also on its past (or sometimes future) values. Unlike ordinary differential equations that relate a function to its immediate derivatives, FDEs involve delays or advances, capturing systems where history influences present behavior. They are used in fields like biology, engineering, and economics to model processes with memory or time-dependent effects, recognizing that current outcomes often depend on earlier conditions, not just the present.