This book presents a new theory for evolution operators and a new
method for defining fractional powers of vector operators. This new
approach allows to define new classes of fractional diffusion and
evolution problems. These innovative methods and techniques, based
on the concept of S-spectrum, can inspire researchers from various
areas of operator theory and PDEs to explore new research
directions in their fields. This monograph is the natural
continuation of the book: Spectral Theory on the S-Spectrum for
Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and
David P. Kimsey (Operator Theory: Advances and Applications, Vol.
270).
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