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A note on short memory principle of fractional calculus

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Abstract

In this paper, from the classical short memory principle under Grünwald-Letnikov definition, several novel short memory principles are presented and investigated. On one hand, the classical principle is extended to Riemann-Liouville and Caputo cases. On the other hand, a special kind of principles are formulated by introducing a discrete argument instead of the continuous time, resulting in principles with fixed memory length or fixed memory step. Apart from these, several interesting properties of the proposed principles are revealed profoundly.

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Authors and Affiliations

  1. Vibration Control and Vehicle Control (VCVC), Lab Dept. of Automation, University of Science and Technology of China, No. 443 Huang Shan Rd., Shu Shan District, Hefei, 230027, P.R. China

    Yiheng Wei, Yuquan Chen, Songsong Cheng & Yong Wang

Authors
  1. Yiheng Wei
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  2. Yuquan Chen
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  3. Songsong Cheng
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  4. Yong Wang
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Corresponding author

Correspondence to Yiheng Wei.

Additional information

The work described in this paper was fully supported by the National Natural Science Foundation of China (61573332, 61601431), the Fundamental Research Funds for the Central Universities (WK2100100028), the Anhui Provincial Natural Science Foundation (1708085QF141) and the General Financial Grant from the China Postdoctoral Science Foundation (2016M602032).

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Wei, Y., Chen, Y., Cheng, S. et al. A note on short memory principle of fractional calculus. FCAA 20, 1382–1404 (2017). https://doi.org/10.1515/fca-2017-0073

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