A note on the Grünwald–Letnikov fractional-order backward-difference

In this paper, a fractional-order backward-difference equivalent formula is considered. From a Grunwald–Letnikow definition formula of a backward-difference (fractional or integer order) an equivalent form is derived. It may be useful in real time calculations (for instance in the evaluation of digital control strategies) due to the reduction in the number of multiplications and additions. The proposed equivalent form may also improve the correctness of the fractional-order backward-difference value. The investigations are illustrated by a numerical example.