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A novel algebraic characteristic of fractional resolvent families

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Abstract

In this paper, we give a novel one-parameter algebraic functional equation for fractional resolvent families. With the help of this functional equation, we are able to show that all fractional resolvent families, except \(C_0\)-semigroups, are never exponentially stable.

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Acknowledgements

We are grateful to Dr. J. Pastor for some helpful discussions, and for suggesting Remark 3.6(2) and Proposition 4.1. We are also grateful to the referees for a painstaking reading of the paper and for pointing out several inaccuracies.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University Jinjiang College, Meishan, 620860, People’s Republic of China

    Jie Mei

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

    Chuang Chen & Miao Li

Authors
  1. Jie Mei
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  2. Chuang Chen
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  3. Miao Li
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Corresponding author

Correspondence to Chuang Chen.

Additional information

Communicated by Abdelaziz Rhandi.

This project was supported by the NSFC-RFBR Programme of China (No. 11611530677).

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Mei, J., Chen, C. & Li, M. A novel algebraic characteristic of fractional resolvent families. Semigroup Forum 99, 293–302 (2019). https://doi.org/10.1007/s00233-018-9964-z

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  • DOI: https://doi.org/10.1007/s00233-018-9964-z

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