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SpringerBriefs in Mathematics

Advances on Fractional Inequalities

Authors: Anastassiou, George A.

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  • Use primarily the Caputo fractional derivative, as the most important in applications, and we present first fractional differentiation inequalities of Opial type where we involve the so called balanced fractional derivatives
  • Fractional differentiation inequalities 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 applications in acoustic wave propagation in homogeneous porous material, diffusive transport, fluid flow, earthquakes, optics, geology, viscoelastic materials, bio-sciences, dynamical processes in self-similar structures, dynamics of 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
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About this book

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.

Reviews

From the reviews:

“This short monograph is a continuation and complement of the author’s previous book ‘Fractional differentiation inequalities’ … . this monograph is a collection of the author’s recent research papers … . each chapter is self-contained with relevant references and can be read independently of the others. … This book is well written and should be useful to researchers and graduate students.” (S. L. Kalla, Zentralblatt MATH, Vol. 1230, 2012)

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-1-4614-0703-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-1-4614-0702-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Advances on Fractional Inequalities
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
George A. Anastassiou
eBook ISBN
978-1-4614-0703-4
DOI
10.1007/978-1-4614-0703-4
Softcover ISBN
978-1-4614-0702-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 122
Topics

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