Topics in Fractional Differential Equations

  • Saïd Abbas
  • Mouffak Benchohra
  • Gaston M. N'Guérékata
Part of the Developments in Mathematics book series (DEVM, volume 27)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 1-10
  3. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 11-24
  4. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 25-114
  5. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 115-169
  6. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 171-249
  7. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 251-285
  8. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 287-339
  9. Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata
    Pages 341-382
  10. Back Matter
    Pages 383-396

About this book

Introduction

During the last decade, there has been an explosion of interest in fractional dynamics as it was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media. Fractional calculus generalizes integrals and derivatives to non-integer orders and has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. This book is addressed to a wide audience of researchers working with fractional dynamics, including mathematicians, engineers, biologists, and physicists. This timely publication may also be suitable for a graduate level seminar for students studying differential equations.

 

Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. In this book, problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. An historical introduction to fractional calculus will be of general interest to a wide range of researchers. Chapter one contains some preliminary background results. The second Chapter is devoted to fractional order partial functional differential equations. Chapter three is concerned with functional partial differential inclusions, while in the fourth chapter, we consider functional impulsive partial hyperbolic differential equations. Chapter five is concerned with impulsive partial hyperbolic functional differential inclusions. Implicit partial hyperbolic differential equations are considered in Chapter six, and finally in Chapter seven, Riemann-Liouville fractional order integral equations are considered. Each chapter concludes with a section devoted to notes and bibliographical remarks. The work is self-contained but also contains questions and directions for further research.

Keywords

Caputo Fractional derivative Darboux problem Riemann-Liouville Integral equations fractional calculus fractional differential equations hyperbolic partial differential equation

Authors and affiliations

  • Saïd Abbas
    • 1
  • Mouffak Benchohra
    • 2
  • Gaston M. N'Guérékata
    • 3
  1. 1., Laboratoire de MathématiquesUniversité de SaïdaSaïdaAlgeria
  2. 2., Laboratoire de MathématiquesUniversité de Sidi Bel-AbbèsSidi Bel-AbbèsAlgeria
  3. 3., Department of MathematicsMorgan State UniversityBaltimoreUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4036-9
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4035-2
  • Online ISBN 978-1-4614-4036-9
  • Series Print ISSN 1389-2177
  • About this book