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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.- Poincaré 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