The Analysis of Fractional Differential Equations

An Application-Oriented Exposition Using Differential Operators of Caputo Type

  • Kai Diethelm

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

Introduction

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.

Keywords

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

  • Kai Diethelm
    • 1
  1. 1.GNS Gesellschaft für Numerische SimulatiBraunschweigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14574-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-14573-5
  • Online ISBN 978-3-642-14574-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book