New Laguerre filter approximators to the Grünwald-Letnikov fractional difference (Q1955132)

Summary: We present a series of new results in modeling of the Grünwald-Letnikov discrete-time fractional difference by means of discrete-time Laguerre filers. The introduced Laguerre-based difference (LD) and combined fractional/Laguerre-based difference (CFLD) are shown to perfectly approximate its fractional difference original, for fractional order \(\alpha \in (0, 2)\). This paper is culminated with the presentation of finite (combined) fractional/Laguerre-based difference (FFLD), whose excellent approximation performance is illustrated in simulation examples.