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Lecture Notes in Mathematics

The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

Authors: Diethelm, Kai

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  • Provides a detailed mathematical description of the class fractional differential operators that is most important in applications in physics, engineering, etc.
  • Bridges the gap between aspects from pure mathematics and application-oriented questions
  • Contains a solid mathematical foundation on which researchers from outside of mathematics can build their models
  • Is written in a style suitable for use as textbook
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eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-642-14574-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-642-14573-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

Reviews

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)


Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction

    Pages 3-12

    Diethelm, Kai

  • Riemann-Liouville Differential and Integral Operators

    Pages 13-47

    Diethelm, Kai

  • Caputo’s Approach

    Pages 49-65

    Diethelm, Kai

  • Mittag-Leffler Functions

    Pages 67-73

    Diethelm, Kai

  • Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations

    Pages 77-83

    Diethelm, Kai

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-642-14574-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-642-14573-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Analysis of Fractional Differential Equations
Book Subtitle
An Application-Oriented Exposition Using Differential Operators of Caputo Type
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2004
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-14574-2
DOI
10.1007/978-3-642-14574-2
Softcover ISBN
978-3-642-14573-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 247
Number of Illustrations
10 b/w illustrations
Topics