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.
Spis treści
Opial#x2013;Type Inequalities for Functions and Their Ordinary and Canavati Fractional Derivatives.- Canavati Fractional Opial#x2013;Type Inequalities and Fractional Differential Equations.- Riemann#x2014;Liouville Opial#x2014;type Inequalities for Fractional Derivatives.- Opial#x2013;type #x2013;Inequalities for Riemann#x2014;Liouville Fractional Derivatives.- Opial#x2013;Type Inequalities Involving Canavati Fractional Derivatives of Two Functions and Applications.- Opial#x2013;Type Inequalities for Riemann#x2014;Liouville Fractional Derivatives of Two Functions with Applications.- Canavati Fractional Opial#x2013;Type Inequalities for Several Functions and Applications.- Riemann#x2014;Liouville Fractional#x2013;Opial Type Inequalities for Several Functions and Applications.- Converse Canavati Fractional Opial#x2013;Type Inequalities for Several Functions.- Converse Riemann#x2014;Liouville Fractional Opial#x2013;Type Inequalities for Several Functions.- Multivariate Canavati Fractional Taylor Formula.- Multivariate Caputo Fractional Taylor Formula.- Canavati Fractional Multivariate Opial#x2013;Type Inequalities on Spherical Shells.- Riemann#x2014;Liouville Fractional Multivariate Opial#x2013;type inequalities over a spherical shell.- Caputo Fractional Multivariate Opial#x2013;Type Inequalities over a Spherical Shell.- Poincar#x00E9;#x2013;Type Fractional Inequalities.- Various Sobolev#x2013;Type Fractional Inequalities.- General Hilbert#x2014;Pachpatte#x2013;Type Integral Inequalities.- General Multivariate Hilbert#x2014;Pachpatte#x2013;Type Integral Inequalities.- Other Hilbert#x2014;Pachpatte#x2013;Type Fractional Integral Inequalities.- Canavati Fractional and Other Approximation of Csiszar#x2019;s #x2013;Divergence.- Caputo and Riemann#x2014;Liouville Fractional Approximation of Csiszar#x2019;s #x2013;Divergence.- Canavati Fractional Ostrowski#x2013;Type Inequalities.- Multivariate Canavati Fractional Ostrowski#x2013;Type Inequalities.- Caputo Fractional Ostrowski#x2013;Type Inequalities.
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