George A. Anastassiou 
Unification of Fractional Calculi with Applications 

This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners and seminars of the above disciplines, also to be in all science and engineering libraries.

Table des matières

Progress on generalized Hilfer fractional calculus and fractional integral inequalities.- Landau Generalized Hilfer fractional inequalities.- Iyengar-Hilfer generalized fractional inequalities.- Generalized Hilfer-Polya, Hilfer-Ostrowski and Hilfer-Hilbert-Pachpatte fractional inequalities.- Generalized Hilfer Fractional Approximation of Csiszar’s f-Divergence.- Generalized Hilfer fractional self-adjoint operator inequalities.- Essential forward and reverse generalized Hilfer-Hardy fractional inequalities.- Principles of Generalized Prabhakar-Hilfer fractional Calculus and Applications.