Fractional Differentiation Inequalities

  • George A. Anastassiou

Table of contents

  1. Front Matter
    Pages i-xi
  2. George A. Anastassiou
    Pages 1-5
  3. George A. Anastassiou
    Pages 257-268
  4. George A. Anastassiou
    Pages 269-278
  5. George A. Anastassiou
    Pages 445-482
  6. George A. Anastassiou
    Pages 483-504
  7. George A. Anastassiou
    Pages 505-522

About this book

Introduction

Fractional differentiation inequalities are by themselves an important area of research. They have many applications in pure and applied mathematics and many other applied sciences. One of the most important applications is in establishing the uniqueness of a solution in fractional differential equations and systems and in fractional partial differential equations. They also provide upper bounds to the solutions of the above equations.

In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined.

This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful.

Keywords

Differential approximation derivative derivatives differential equation equation form function functions information information theory integral mathematics types

Authors and affiliations

  • George A. Anastassiou
  1. 1.Dept. Mathematical SciencesUniversity of MemphisMemphisU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-98128-4
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-98127-7
  • Online ISBN 978-0-387-98128-4
  • About this book