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29 March 2024
 
  » arxiv » 1901.9211

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Analytical and numerical representations for discrete Grunwald-Letnikov fractional calculus
Yiheng Wei ; Tianyu Liu ; Peter W Tse ; Yong Wang ;
Date 26 Jan 2019
AbstractThis paper focuses on the new representation of Grunwald-Letnikov discrete fractional calculus. By resorting the classical nabla Taylor series, the series representation of Grunwald-Letnikov difference/sum is established. Changing the expanded point from the initial instant to the current time, another series like representation is developed. To improve the practicability, the results are extended to the variable order case and the fixed memory step case. With the new representations, the corresponding Leibniz rules are built subsequently. Simulation study clearly illustrates the effectiveness and efficiency of the proposed theory.
Source arXiv, 1901.9211
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