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.