The theory of fractional powers of operators

By C. Carracedo, M. Alix. 2001

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Periodic solutions of second order differential equations in Banach spaces (2006, methodology): “For further information on positive operators we refer to the recent monograph by Martinez-Sanz [27].”
Hölder continuous solutions for fractional differential equations and maximal regularity (2013, background): “This functional calculus may be extended in a natural way in order to define the fractional powers A for every ε > 0, see [25, 35].”
The blow-up and global existence of solutions of Cauchy problems for a time fractional diffusion equation (2015, background): “Then T (t) is an analytic and contractive semigroup on C0(R ) [3], [22] and, for t > 0, x ∈ R , (2.”
On fractional powers of generators of fractional resolvent families (2010, methodology): “By using the theory of functional calculus for sectorial operators (see [4,14, 21,26]), we are able to give positive answers to the questions above.”