Remarks on five equivalent forms of the fractional – order backward

Ostalczyk, Piotr2016-02-052016-02-052014Bulletin of the Polish Academy of Sciences Technical Sciences, Vol. 62, Issue 2,2014, pages 271–278http://hdl.handle.net/11652/1118http://www.degruyter.com/view/j/bpasts.2014.62.issue-2/bpasts-2014-0027/bpasts-2014-0027.xml?format=INTIn this paper a fractional-order backward-difference/sum (FOBD/S) equivalent formulae are considered. From the Gr¨unwald- Letnikov (GL - FOBD) definition formula and its Horner equivalent form one derives the Riemann-Liouville FOBD (RL - FOBD). Also the Caputo and polynomial-like forms are defined. All forms may be useful in real-time calculations (in the evaluation of digital control strategies) due to the reduction of fractional orders. The investigations are illustrated by a numerical example.endiscrete systemsfractional - order backward difference/sumRemarks on five equivalent forms of the fractional – order backward – differenceArtykuł