Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes, Fabrizio Colombo; Jonathan Gantner

Автор: Fudong Ge; YangQuan Chen; Chunhai Kou
Название: Regional Analysis of Time-Fractional Diffusion Processes
ISBN: 3319892193 ISBN-13(EAN): 9783319892191
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest. The book’s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security. Academics and graduate students working with cyber-physical and distributed systems or interested in the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research.

Автор: Fabrizio Colombo; Jonathan Gantner; David P. Kimse
Название: Spectral Theory on the S-Spectrum for Quaternionic Operators
ISBN: 3030030733 ISBN-13(EAN): 9783030030735
Издательство: Springer
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Цена: 11878.00 р.
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Описание: The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.