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The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

  • Book
  • © 2010

Overview

Authors:
  1. Kai Diethelm

    1. GNS Gesellschaft für Numerische Simulati, Braunschweig, Germany

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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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. Fundamentals of Fractional Calculus

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Kai Diethelm
      Pages 3-12

    3. Riemann-Liouville Differential and Integral Operators

      • Kai Diethelm
      Pages 13-47

    4. Caputo’s Approach

      • Kai Diethelm
      Pages 49-65

    5. Mittag-Leffler Functions

      • Kai Diethelm
      Pages 67-73

  4. Back Matter

    Pages 187-253
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Keywords

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)

Authors and Affiliations

  • GNS Gesellschaft für Numerische Simulati, Braunschweig, Germany

    Kai Diethelm

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: https://doi.org/10.1007/978-3-642-14574-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Softcover ISBN: 978-3-642-14573-5Published: 03 September 2010

  • eBook ISBN: 978-3-642-14574-2Published: 18 August 2010

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 247

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Ordinary Differential Equations, Integral Equations, Analysis

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