Integer/fractional decomposition of the impulse response of fractional linear systems

•Application of fractional calculus to nonlinear signals and systems.•Generalization of describing function.•Limit cycle and signal propagation model using fractional describing function.

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.