Introduction to Functional Differential Equations

There are different types of functional differential equations (FDEs) arising from important applications: delay differential equations (DDEs) (also referred to as retarded FDEs [RFDEs]), neutral FDEs (NFDEs), and mixed FDEs (MFDEs). The classification depends on how the current change rate of the system state depends on the history (the historical status of the state only or the historical change rate and the historical status) or whether the current change rate of the system state depends on the future expectation of the system. Later we will also see that the delay involved may also depend on the system state, leading to DDEs with state-dependent delay.

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