Constructive Fractional Analysis with Applications - Anastassiou, George A.

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Résumé :
This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss?Weierstrass, Poisson?Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann?Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert?Pachpatte and on the spherical shell. He continues with E. R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.

Biographie:
George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including Fractional Differentiation Inequalities (c) 2009, Fuzzy Mathematics: Approximation Theory (c) 2010, Intelligent Systems: Approximation by Artificial Neural Networks (c) 2014, The History of Approximation Theory (c) 2005, Modern Differential Geometry in Gauge Theories (c) 2006, and more. Razvan Alex Mezei received his PhD from the University of Memphis and currently holds an assistant professorship and Lenoir-Rhyne University, Hickory, North Carolina. He teaches mathematics as well as computer science/IT courses to undergraduates and is a computing sciences program coordinator. Mezei has extensive experience in computer programming and software development and has written several publications with George Anastassiou....

Sommaire:
Variable order general fractional integral inequalitie.- Variable order fractional integral inequalities for spherical shell.- Left fractional integral inequalities of E.R. Love type.- Right side fractional integral inequalities of E.R. Love type.- General fractional Landau inequalities.- Abstract fractional Landau inequalities.- Fractional Landau inequalities of Riemann-Liouville type.- Generalized Canavati fractional Landau inequalities.- Sequential left abstract fractional Landau inequalities.- Iterated left abstract generalized fractional Landau inequalities.