Regional analysis of time-fractional diffusion processes / Fudong Ge, YangQuan Chen, Chunhai Kou.
Ge, Fudong, author.; Chen, YangQuan, 1966- author.; Kou, Chunhai, author.
2018
QA274.75
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Title
Regional analysis of time-fractional diffusion processes / Fudong Ge, YangQuan Chen, Chunhai Kou.
Author
Ge, Fudong, author.
ISBN
9783319728964 (electronic book)
3319728962 (electronic book)
9783319728957
3319728954
DOI
https://doi.org/10.1007/978-3-319-72896-4
Published
Cham, Switzerland : Springer, [2018]
Copyright
©2018
Language
English
Description
1 online resource
Item Number
10.1007/978-3-319-72896-4 doi
Call Number
QA274.75
Dewey Decimal Classification
519.233
Summary
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 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.
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Includes bibliographical references and index.
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Access limited to authorized users.
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text file PDF
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Vendor-supplied metadata.
Added Author
Chen, YangQuan, 1966- author.
Kou, Chunhai, author.
Available in Other Form
Regional analysis of time-fractional diffusion processes.
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Intro; Preface; Acknowledgements; Contents; Abbreviations; List of Figures; 1 Introduction; 1.1 Cyber-Physical Systems and Distributed Parameter Systems; 1.1.1 Cyber-Physical Systems; 1.1.2 Distributed Parameter Systems; 1.2 New Challenges; 1.3 Continuous Time Random Walk and Fractional Dynamics Approach; 1.3.1 Continuous Time Random Walk; 1.3.2 Fractional Dynamics Approach; 1.4 Regional Analysis via Actuators and Sensors; 1.4.1 Actuators; 1.4.2 Sensors; 1.4.3 Regional Analysis and the Emerging Research Opportunities; References; 2 Preliminary Results.

2.1 Special Functions and Their Properties2.1.1 The Gamma Function and Its Related Special Functions; 2.1.2 The Mittag-Leffler Functions and Their Properties; 2.2 Fractional Calculus; 2.2.1 Backgrounds; 2.2.2 Riemann
Liouville Fractional Integrals; 2.2.3 Riemann
Liouville Fractional Derivatives; 2.2.4 Caputo Fractional Derivatives; 2.3 C0-Semigroups; 2.4 Hilbert Uniqueness Methods; References; 3 Regional Controllability; 3.1 Regional Controllability; 3.1.1 Riemann
Liouville-Type Time Fractional Diffusion Systems; 3.1.2 Caputo-Type Time Fractional Diffusion Systems.

3.2 Regional Gradient Controllability3.2.1 Riemann
Liouville-Type Time Fractional Diffusion Systems; 3.2.2 Caputo-Type Time Fractional Diffusion Systems; 3.3 Regional Boundary Controllability; 3.3.1 Riemann
Liouville-Type Time Fractional Diffusion Systems; 3.3.2 Caputo-Type Time Fractional Diffusion Systems; 3.4 Notes and Remarks; References; 4 Regional Observability; 4.1 Regional Observability; 4.1.1 Riemann
Liouville-Type Time Fractional Diffusion Systems; 4.1.2 Caputo-Type Time Fractional Diffusion Systems; 4.2 Regional Gradient Observability.

4.2.1 Riemann
Liouville-Type Time Fractional Diffusion Systems4.2.2 Caputo-Type Time Fractional Diffusion Systems; 4.3 Regional Boundary Observability; 4.3.1 Riemann
Liouville-Type Time Fractional Diffusion Systems; 4.3.2 Caputo-Type Time Fractional Diffusion Systems; 4.4 Notes and Remarks; References; 5 Regional Detection of Unknown Sources; 5.1 Preliminary Results; 5.1.1 Sources; 5.1.2 Detection; 5.2 Riemannâ#x80;#x93;Liouville-Type Time Fractional Diffusion Systems; 5.2.1 Problem Statement; 5.2.2 Regional Strategic Sensors and Regional Spy Sensors.

5.2.3 Reconstruction of a Regionally Detectable Source5.2.4 Several Examples; 5.3 Caputo-Type Time Fractional Diffusion Systems; 5.3.1 Problem Formulation; 5.3.2 The Relationships Between Strategic Sensors and Spy Sensors in Ï#x89;; 5.3.3 An Approach to Regionally Detect the Source; 5.3.4 An Example; 5.4 Notes and Remarks; References; 6 Spreadability; 6.1 The Basic Knowledge of Spreadability; 6.2 Riemann
Liouville-Type Time Fractional Diffusion Systems; 6.2.1 Spreading Control Problem; 6.2.2 Adaptive Spreading Control Problems; 6.3 Caputo-Type Time Fractional Diffusion Systems.

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