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000825643 019__ $$a1019640492$$a1019745602$$a1021202832$$a1026625174
000825643 020__ $$a9783319728964$$q(electronic book)
000825643 020__ $$a3319728962$$q(electronic book)
000825643 020__ $$z9783319728957
000825643 020__ $$z3319728954
000825643 0247_ $$a10.1007/978-3-319-72896-4$$2doi
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000825643 049__ $$aISEA
000825643 050_4 $$aQA274.75
000825643 08204 $$a519.233$$223
000825643 1001_ $$aGe, Fudong,$$eauthor.
000825643 24510 $$aRegional analysis of time-fractional diffusion processes /$$cFudong Ge, YangQuan Chen, Chunhai Kou.
000825643 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2018]
000825643 264_4 $$c©2018
000825643 300__ $$a1 online resource
000825643 336__ $$atext$$btxt$$2rdacontent
000825643 337__ $$acomputer$$bc$$2rdamedia
000825643 338__ $$aonline resource$$bcr$$2rdacarrier
000825643 347__ $$atext file$$bPDF$$2rda
000825643 504__ $$aIncludes bibliographical references and index.
000825643 5050_ $$aIntro; Preface; Acknowledgements; Contents; Abbreviations; List of Figures; 1 Introduction; 1.1 Cyber-Physical Systems and Distributed Parameter Systems; 1.1.1 Cyber-Physical Systems; 1.1.2 Distributed Parameter Systems; 1.2 New Challenges; 1.3 Continuous Time Random Walk and Fractional Dynamics Approach; 1.3.1 Continuous Time Random Walk; 1.3.2 Fractional Dynamics Approach; 1.4 Regional Analysis via Actuators and Sensors; 1.4.1 Actuators; 1.4.2 Sensors; 1.4.3 Regional Analysis and the Emerging Research Opportunities; References; 2 Preliminary Results.
000825643 5058_ $$a2.1 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.
000825643 5058_ $$a3.2 Regional Gradient Controllability3.2.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 3.2.2 Caputo-Type Time Fractional Diffusion Systems; 3.3 Regional Boundary Controllability; 3.3.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 3.3.2 Caputo-Type Time Fractional Diffusion Systems; 3.4 Notes and Remarks; References; 4 Regional Observability; 4.1 Regional Observability; 4.1.1 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 4.1.2 Caputo-Type Time Fractional Diffusion Systems; 4.2 Regional Gradient Observability.
000825643 5058_ $$a4.2.1 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.
000825643 5058_ $$a5.2.3 Reconstruction of a Regionally Detectable Source5.2.4 Several Examples; 5.3 Caputo-Type Time Fractional Diffusion Systems; 5.3.1 Problem Formulation; 5.3.2 The Relationships Between Strategic Sensors and Spy Sensors in Ï#x89;; 5.3.3 An Approach to Regionally Detect the Source; 5.3.4 An Example; 5.4 Notes and Remarks; References; 6 Spreadability; 6.1 The Basic Knowledge of Spreadability; 6.2 Riemann -- Liouville-Type Time Fractional Diffusion Systems; 6.2.1 Spreading Control Problem; 6.2.2 Adaptive Spreading Control Problems; 6.3 Caputo-Type Time Fractional Diffusion Systems.
000825643 506__ $$aAccess limited to authorized users.
000825643 520__ $$aThis monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest. The book?s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security. Academics and graduate students working with cyber-physical and distributed systems or interested in the the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research.
000825643 588__ $$aVendor-supplied metadata.
000825643 650_0 $$aDiffusion processes.
000825643 650_0 $$aCooperating objects (Computer systems)
000825643 650_0 $$aDistributed parameter systems.
000825643 7001_ $$aChen, YangQuan,$$d1966-$$eauthor.
000825643 7001_ $$aKou, Chunhai,$$eauthor.
000825643 77608 $$iPrint version:$$aGe, Fudong.$$tRegional analysis of time-fractional diffusion processes.$$dCham, Switzerland : Springer, [2018]$$z3319728954$$z9783319728957$$w(OCoLC)1013170960
000825643 852__ $$bebk
000825643 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-72896-4$$zOnline Access$$91397441.1
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000825643 980__ $$aBIB
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000825643 983__ $$aOnline
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