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Fractional differentiation inequalities

Author: George A Anastassiou
Publisher: Dordrecht ; New York : Springer, ©2009.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book presents the Opial, Poincare, Sobolev, Hilbert and Ostrowski fractional differentiation equalities, and results are derived for each using three different types of fractional derivatives.  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: George A Anastassiou
ISBN: 9780387981277 0387981276 9780387981284 0387981284
OCLC Number: 426116706
Description: xiv, 675 pages ; 25 cm
Contents: Introduction.- Opial Type Inequalities for Functions and Their Ordinary and Canavati Fractional Derivatives.- Canavati Fractional Opial Type Inequalities and Fractional Differential Equations.- Riemann-Liouville Opial Type Inequalities for Fractional Derivatives.- Opial Type L^p-Inequalities for Riemann-Liouville Fractional Derivatives.- Opial Type Inequalities Involving Canavati Fractional Derivatives of Two Functions and Applications.- Opial Type Inequalities for Riemann-Liouville Fractional Derivatives of Two Functions with Applications.- Canavati Fractional Opial Type Inequalities for Several Functions and Applications.- Riemann-Liouville Fractional Opial Type Inequalities for Several Functions and Applications.- Converse Canavati Fractional Opial Type Inequalities for Several Functions.- Converse Riemann-Liouville Fractional Opial Type Inequalities for Several Functions.- Multivariate Canavati Fractional Taylor Formula.- Multivariate Caputo Fractional Taylor Formula.- Canavati Fractional Multivariate Opial Type Inequalities on Spherical Shells.- Riemann-Liouville Fractional Multivariate Opial Type Inequalities Over a Spherical Shell.- Caputo Fractional Multivariate Opial Type Inequalities Over a Spherical Shell.- Poincare Type Fractional Inequalities.- Various Sobolev Type Fractional Inequalities.- General Hilbert-Pachpatte Type Inequalities.- General Multivariate Hilbert-Pachpatte Type Integral Inequalties.- Other Hilbert-Pachpatte Type Fractional Interal Inequalities.- Canavati Fractional and Other Approximation of Csiszar's f-Divergence.- Caputo and Riemann-Liouville Fractional Approximation of Csiszar's f-Divergence.- Canavati Fractional Ostrowski Type Inequalities.- Multivariate Canavati Fractional Ostrowski Type Inequalities.- Caputo Fractional Ostrowski Type Inequalities.- Appendix.- References.- List of Symbols.- Index
Responsibility: George A. Anastassiou.

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From the review:"Professor Anastassiou considers three definitions of fractional derivatives. ... The list of references runs to four hundred and twelve items. ... for a specialist in fractional Read more...

 
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