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Regional Analysis of Time-Fractional Diffusion Processes

  • Fudong Ge
  • YangQuan Chen
  • Chunhai Kou
Book

Table of contents

  1. Front Matter
    Pages i-xix
  2. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 1-16
  3. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 17-44
  4. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 45-120
  5. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 121-180
  6. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 181-197
  7. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 199-213
  8. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 215-232
  9. Fudong Ge, YangQuan Chen, Chunhai Kou
    Pages 233-248
  10. Back Matter
    Pages 249-250

About this book

Introduction

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.

Keywords

Fractional Calculus Anomalous Diffusion Processes Regional Analysis Sensors and Actuators General Distributed Parameter Systems

Authors and affiliations

  • Fudong Ge
    • 1
  • YangQuan Chen
    • 2
  • Chunhai Kou
    • 3
  1. 1.School of Computer ScienceChina University of GeosciencesWuhanChina
  2. 2.Department of Mechanical Engineering (MESA-Lab)University of California, MercedMercedUSA
  3. 3.Department of Applied MathematicsDonghua UniversityShanghaiChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-72896-4
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-72895-7
  • Online ISBN 978-3-319-72896-4
  • Buy this book on publisher's site