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
    2. Duarte Valério, José Sá da Costa
      Pages 229-242
    3. Laurent Sommacal, Pierre Melchior, Jean-Marie Cabelguen, Alain Oustaloup, Auke Ijspeert
      Pages 271-285
    4. Pascal Serrier, Xavier Moreau, Alain Oustaloup
      Pages 287-302
  6. Electrical Systems

    1. Front Matter
      Pages 303-303
    2. Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha
      Pages 305-322
    3. J. A. Tenreiro Machado, Isabel S. Jesus, Alexandra Galhano, J. Boaventura Cunha, J. K. Tar
      Pages 323-332
    4. Cindy X. Jiang, Joan E. Carletta, Tom T. Hartley
      Pages 333-346
    5. Jay L. Adams, Tom T. Hartley, Carl F. Lorenzo
      Pages 347-360
  7. Viscoelastic and Disordered Media

    1. Front Matter
      Pages 361-361
    2. R. R. Nigmatullin, A. P. Alekhin
      Pages 377-388
    3. Satwinder Jit Singh, Anindya Chatterjee
      Pages 389-402
  8. Control

    1. Front Matter
      Pages 417-417
    2. Mathieu Moze, Jocelyn Sabatier, Alain Oustaloup
      Pages 419-434
    3. Vicente Feliu, Blas M. Vinagre, Concepción A. Monje
      Pages 449-462
    4. Duarte Valério, José Sá da Costa
      Pages 463-476
    5. Pierre Melchior, Alexandre Poty, Alain Oustaloup
      Pages 477-492
    6. Pierre Melchior, Mikaël Cugnet, Jocelyn Sabatier, Alexandre Poty, Alain Oustaloup
      Pages 493-509
    7. Patrick Lanusse, Alain Oustaloup, Jocelyn Sabatier
      Pages 527-542

About this book


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.


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

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