Analytical and numerical representations for discrete Grünwald-Letnikov fractional calculus

Yiheng Wei; YangQuan Chen; Peter W Tse; Songsong Cheng

doi:10.1109/CAC51589.2020.9327090

Analytical and numerical representations for discrete Grünwald-Letnikov fractional calculus

Yiheng Wei, YangQuan Chen, Peter W Tse, Songsong Cheng

College of Engineering

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

2 Citations (Scopus)

Abstract

This paper focuses on the new representation of discrete Grünwald-Letnikov fractional calculus. By resorting the classical nabla Taylor formula and nabla Taylor series, the representations of Grünwald-Letnikov difference/sum are 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 developed representations, the corresponding Leibniz rules are built subsequently.

Original language	English
Title of host publication	Proceedings 2020 Chinese Automation Congress (CAC 2020)
Publisher	IEEE
Pages	2097-2102
ISBN (Electronic)	9781728176871
ISBN (Print)	9781728176888
DOIs	https://doi.org/10.1109/CAC51589.2020.9327090
Publication status	Published - Nov 2020
Event	2020 Chinese Automation Congress (CAC 2020) - Shanghai, China Duration: 6 Nov 2020 → 8 Nov 2020

Publication series

Name	Proceedings - Chinese Automation Congress, CAC
ISSN (Print)	2688-092X
ISSN (Electronic)	2688-0938

Conference

Conference	2020 Chinese Automation Congress (CAC 2020)
Abbreviated title	CAC 2020
Place	China
City	Shanghai
Period	6/11/20 → 8/11/20

Research Keywords

Discrete fractional calculus
Grünwald-Letnikov definition
Series representation
Short memory principle
Variable order case

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10.1109/CAC51589.2020.9327090

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@inproceedings{dd916eef75bd4ac18fc3522aa58775b6,

title = "Analytical and numerical representations for discrete Gr{\"u}nwald-Letnikov fractional calculus",

abstract = "This paper focuses on the new representation of discrete Gr{\"u}nwald-Letnikov fractional calculus. By resorting the classical nabla Taylor formula and nabla Taylor series, the representations of Gr{\"u}nwald-Letnikov difference/sum are 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 developed representations, the corresponding Leibniz rules are built subsequently.",

keywords = "Discrete fractional calculus, Gr{\"u}nwald-Letnikov definition, Series representation, Short memory principle, Variable order case",

author = "Yiheng Wei and YangQuan Chen and Tse, {Peter W} and Songsong Cheng",

year = "2020",

month = nov,

doi = "10.1109/CAC51589.2020.9327090",

language = "English",

isbn = "9781728176888",

series = "Proceedings - Chinese Automation Congress, CAC",

publisher = "IEEE",

pages = "2097--2102",

booktitle = "Proceedings 2020 Chinese Automation Congress (CAC 2020)",

address = "United States",

note = "2020 Chinese Automation Congress (CAC 2020), CAC 2020 ; Conference date: 06-11-2020 Through 08-11-2020",

}

Wei, Y, Chen, Y, Tse, PW & Cheng, S 2020, Analytical and numerical representations for discrete Grünwald-Letnikov fractional calculus. in Proceedings 2020 Chinese Automation Congress (CAC 2020)., 9327090, Proceedings - Chinese Automation Congress, CAC, IEEE, pp. 2097-2102, 2020 Chinese Automation Congress (CAC 2020), Shanghai, China, 6/11/20. https://doi.org/10.1109/CAC51589.2020.9327090

Analytical and numerical representations for discrete Grünwald-Letnikov fractional calculus. / Wei, Yiheng; Chen, YangQuan; Tse, Peter W et al.
Proceedings 2020 Chinese Automation Congress (CAC 2020). IEEE, 2020. p. 2097-2102 9327090 (Proceedings - Chinese Automation Congress, CAC).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Analytical and numerical representations for discrete Grünwald-Letnikov fractional calculus

AU - Wei, Yiheng

AU - Chen, YangQuan

AU - Tse, Peter W

AU - Cheng, Songsong

PY - 2020/11

Y1 - 2020/11

N2 - This paper focuses on the new representation of discrete Grünwald-Letnikov fractional calculus. By resorting the classical nabla Taylor formula and nabla Taylor series, the representations of Grünwald-Letnikov difference/sum are 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 developed representations, the corresponding Leibniz rules are built subsequently.

AB - This paper focuses on the new representation of discrete Grünwald-Letnikov fractional calculus. By resorting the classical nabla Taylor formula and nabla Taylor series, the representations of Grünwald-Letnikov difference/sum are 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 developed representations, the corresponding Leibniz rules are built subsequently.

KW - Discrete fractional calculus

KW - Grünwald-Letnikov definition

KW - Series representation

KW - Short memory principle

KW - Variable order case

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85100935657&origin=recordpage

U2 - 10.1109/CAC51589.2020.9327090

DO - 10.1109/CAC51589.2020.9327090

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9781728176888

T3 - Proceedings - Chinese Automation Congress, CAC

SP - 2097

EP - 2102

BT - Proceedings 2020 Chinese Automation Congress (CAC 2020)

PB - IEEE

T2 - 2020 Chinese Automation Congress (CAC 2020)

Y2 - 6 November 2020 through 8 November 2020

ER -

Analytical and numerical representations for discrete Grünwald-Letnikov fractional calculus

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