Advances in Fractional Calculus

Theoretical Developments and Applications in Physics and Engineering

  • Jocelyn Sabatier
  • Om Prakash Agrawal
  • J. A. Tenreiro Machado

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Analytical and Numerical Techniques

    1. Front Matter
      Pages 1-1
    2. Satwinder Jit Singh, Anindya Chatterjee
      Pages 3-14
    3. John W. Hanneken, David M. Vaught, B. N. Narahari Achar
      Pages 15-26
    4. B. N. Narahari Achar, Carl F. Lorenzo, Tom T. Hartley
      Pages 27-42
    5. Blanca Bonilla, Margarita Rivero, Juan J. Trujillo
      Pages 77-91
    6. Manuel Duarte Ortigueira
      Pages 93-112
  3. Classical Mechanics and Particle Physics

    1. Front Matter
      Pages 113-113
    2. Dumitru Baleanu, Sami I. Muslih
      Pages 115-126
    3. Raoul R. Nigmatullin, Juan J. Trujillo
      Pages 155-167
  4. Diffusive Systems

    1. Front Matter
      Pages 169-169
    2. N. Krepysheva, L. Di Pietro, M. C. Néel
      Pages 171-184
    3. Kira Logvinova, Marie Christine Néel
      Pages 185-197
    4. F. San Jose Martinez, Y. A. Pachepsky, W. J. Rawls
      Pages 199-212
    5. Amel Benchellal, Thierry Poinot, Jean-Claude Trigeassou
      Pages 213-225
  5. Modeling

    1. Front Matter
      Pages 227-227

About this book

Introduction

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Keywords

Potential Signal Vibration calculus cognition design differentiation and integration of arbitrary order electricity fractional derivatives and their applications image processing mechanics model modeling operator system

Editors and affiliations

  • Jocelyn Sabatier
    • 1
  • Om Prakash Agrawal
    • 2
  • J. A. Tenreiro Machado
    • 3
  1. 1.Université Bordeaux 1, – ENSEIRBFrance
  2. 2.Southern Illinois UniversityCarbondaleUSA
  3. 3.Institute of Engineering of PortoPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-6042-7
  • Copyright Information Springer Netherlands 2007
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-1-4020-6041-0
  • Online ISBN 978-1-4020-6042-7
  • About this book