A novel algebraic characteristic of fractional resolvent families
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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.
KeywordsFractional resolvent families Fractional Cauchy problems Algebraic functional equation Laplace transform Exponential stability
- 2.Bajlekova, E.: Fractional Evolution Equations in Banach Spaces. Ph.D. Thesis, Eindhoven University of Technology (2001)Google Scholar