Fractional discrete-time linear systems

In this paper, the class of discrete linear systems is enlarged with the inclusion of the discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how to compute the impulse response and transfer function. The theory is supported by the Cauchy integrals that perform projections of the frequency response into or outside the unit circle. The presented formalism is similar to that usually followed.