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Advances on Fractional Inequalities

  • George A.¬†Anastassiou

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. George A. Anastassiou
    Pages 41-49
  3. George A. Anastassiou
    Pages 63-75
  4. George A. Anastassiou
    Pages 77-84
  5. George A. Anastassiou
    Pages 85-91
  6. George A. Anastassiou
    Pages 93-99
  7. George A. Anastassiou
    Pages 101-111
  8. George A. Anastassiou
    Pages 113-121

About this book

Introduction

Advances on Fractional Inequalities  use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which  involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given.

Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations.

Fractional Calculus has emerged as very useful over the last forty years due to its many applications in almost all applied sciences. This is currently seen in applications in acoustic wave propagation in inhomogeneous porous material, diffusive transport, fluid flow, dynamical processes in self-similar structures, dynamics of earthquakes, optics, geology, viscoelastic materials, bio-sciences, bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etc. Almost all fields of research in science and engineering use fractional calculus in order to describe results.

This book is a part of Fractional Calculus, therefore it  is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering and all other applied sciences.

Keywords

Caputo fractional derivative Fractional Calculus Fractional differentiation inequalities Opial type Ostrowski inequalities

Authors and affiliations

  • George A.¬†Anastassiou
    • 1
  1. 1., Department of Mathematical SciencesUniversity of MemphisMEMPHISUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0703-4
  • Copyright Information George A. Anastassiou 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-0702-7
  • Online ISBN 978-1-4614-0703-4
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site