Semigroup Forum

, Volume 99, Issue 2, pp 293–302 | Cite as

A novel algebraic characteristic of fractional resolvent families

  • Jie Mei
  • Chuang ChenEmail author
  • Miao Li
Research Article


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.


Fractional resolvent families Fractional Cauchy problems Algebraic functional equation Laplace transform Exponential stability 



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. 1.Department of MathematicsSichuan University Jinjiang CollegeMeishanPeople’s Republic of China
  2. 2.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China

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