On fractional powers of generators of fractional resolvent families
By Miao Li, Chuang Chen, Fubo Li. 2010
120 citations recorded by the source corpus.
Abstract We show that if −A generates a bounded α-times resolvent family for some α ∈ ( 0 , 2 ] , then − A β generates an analytic γ-times resolvent family for β ∈ ( 0 , 2 π − π γ 2 π − π α ) and γ ∈ ( 0 , 2 ) . And a generalized subordination principle is derived. In particular, if −A generates a bounded α-times resolvent family for some α ∈ ( 1 , 2 ] , then − A 1 / α generates an analytic C 0 -semigroup. Such relations are applied to study the solutions of Cauchy problems of fractional order and first order.
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Citations in the corpus
- Hölder continuous solutions for fractional differential equations and maximal regularity (2013, background): “approaches to the existence and uniqueness of solutions to fractional differential equations can be found, for example, in [6, 9, 13, 17, 20, 32].”
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- A blowup alternative result for fractional nonautonomous evolution equation of Volterra type (2018, background): “For more details, see [2, 4, 6, 8, 9, 11, 12], [18]-[22], [28]-[32] and the references therein for more comments and citations.”
- The blow-up and global existence of solutions of Cauchy problems for a time fractional diffusion equation (2015, background): “Recently, there are many papers about the existence and properties of solutions for the fractional abstract Cauchy problem, see for example [26], [15], [29], [20] and the references therein.”
- Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators (2020, background): “The more properties about α-order solution operator and α-order resolvent operator are also discussed by Chen, Li and Li in [11], Chen, Zhang and Li in [12], Li, Chen and Li in [26] and Li, Peng and Jia in [29].”