© 2010

The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type


Part of the Lecture Notes in Mathematics book series (LNM, volume 2004)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Fundamentals of Fractional Calculus

    1. Front Matter
      Pages 1-1
    2. Kai Diethelm
      Pages 3-12
    3. Kai Diethelm
      Pages 49-65
    4. Kai Diethelm
      Pages 67-73
  3. Theory of Fractional Differential Equations

  4. Back Matter
    Pages 187-253

About this book


Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.


Derivative Mittag-Leffler functions calculus differential equation existence, uniqueness and stability of solutions fractional derivative of Caputo type fractional differential equation single- and multi-term differential equations

Authors and affiliations

  1. 1.GNS Gesellschaft für Numerische SimulatiBraunschweigGermany

Bibliographic information

  • Book Title The Analysis of Fractional Differential Equations
  • Book Subtitle An Application-Oriented Exposition Using Differential Operators of Caputo Type
  • Authors Kai Diethelm
  • Series Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-642-14573-5
  • eBook ISBN 978-3-642-14574-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VIII, 247
  • Number of Illustrations 10 b/w illustrations, 0 illustrations in colour
  • Topics Ordinary Differential Equations
    Integral Equations
  • Buy this book on publisher's site


From the reviews:

“This book treats a fast growing field of fractional differential equations, i.e., differential equations with derivatives of non-integer order. … The book consists of two parts, eight chapters, an appendix, references and an index. … The book is well written and easy to read. It could be used for, a course in the application of fractional calculus for students of applied mathematics and engineering.” (Teodor M. Atanacković, Mathematical Reviews, Issue 2011 j)

“This monograph is intended for use by graduate students, mathematicians and applied scientists who have an interest in fractional differential equations. The Caputo derivative is the main focus of the book, because of its relevance to applications. … The monograph may be regarded as a fairly self-contained reference work and a comprehensive overview of the current state of the art. It contains many results and insights brought together for the first time, including some new material that has not, to my knowledge, appeared elsewhere.” (Neville Ford, Zentralblatt MATH, Vol. 1215, 2011)