Overview
- 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
- Covers a maximum number of cases in various applications
- Includes constructive approximation theory
Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 362)
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About this book
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.
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Table of contents (26 chapters)
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Front Matter
Authors and Affiliations
Bibliographic Information
Book Title: Constructive Fractional Analysis with Applications
Authors: George A. Anastassiou
Series Title: Studies in Systems, Decision and Control
DOI: https://doi.org/10.1007/978-3-030-71481-9
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-71480-2Published: 02 April 2021
Softcover ISBN: 978-3-030-71483-3Published: 02 April 2022
eBook ISBN: 978-3-030-71481-9Published: 01 April 2021
Series ISSN: 2198-4182
Series E-ISSN: 2198-4190
Edition Number: 1
Number of Pages: XV, 522
Number of Illustrations: 1 b/w illustrations
Topics: Computational Intelligence, Complex Systems, Algorithm Analysis and Problem Complexity