Research Papers

A New Insight Into the Grünwald–Letnikov Discrete Fractional Calculus

[+] Author and Article Information
Yiheng Wei, Weidi Yin, Yanting Zhao

Department of Automation,
University of Science and Technology of China,
Hefei 230026, China

Yong Wang

Department of Automation,
University of Science and Technology of China,
Hefei 230026, China
e-mail: yongwang@ustc.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 31, 2018; final manuscript received January 17, 2019; published online February 15, 2019. Assoc. Editor: Firdaus Udwadia.

J. Comput. Nonlinear Dynam 14(4), 041008 (Feb 15, 2019) (5 pages) Paper No: CND-18-1343; doi: 10.1115/1.4042635 History: Received July 31, 2018; Revised January 17, 2019

The primary work of this paper is to investigate some potential properties of Grünwald–Letnikov discrete fractional calculus. By employing a concise and convenient description, this paper not only establishes excellent relationships between fractional difference/sum and the integer order case but also generalizes the Z-transform and convolution operation.

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