Regional analysis of time-fractional diffusion processes. ([2018])

• Record Type: Book
• Further Information: Note: Fudong Ge, YangQuan Chen, Chunhai Kou.
• Authors: Ge, Fudong; Chen, YangQuan, 1966-; Kou, Chunhai
• Contents: 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 519.233; Engineering; Diffusion processes; Cooperating objects (Computer systems); Distributed parameter systems; MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Cooperating objects (Computer systems); Diffusion processes; Distributed parameter systems; Mathematics -- Functional Analysis; Science -- System Theory; Functional analysis & transforms; Cybernetics & systems theory; Operator theory; Systems theory; Technology & Engineering -- Automation; Automatic control engineering; Electronic books
• Languages: English
• ISBNs: 9783319728964; 3319728962
• Related ISBNs: 9783319728957; 3319728954
• Notes: Note: Includes bibliographical references and index.; Note: Vendor-supplied metadata.
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