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Constructive Fractional Analysis with Applications

  • Book
  • © 2021

Overview

Authors:
  1. George A. Anastassiou

    1. Department of Mathematical Sciences, University of Memphis, Memphis, USA

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  • 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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Table of contents (26 chapters)

  1. A Study of Gronwall Inequalities of Fractional Variable Order

    • George A. Anastassiou
    Pages 315-332

  2. General Ordinary and Fractional Approximation with Positive Sublinear Operators

    • George A. Anastassiou
    Pages 333-351

  3. Complete Approximations with Multivariate Generalized Picard Singular Integrals

    • George A. Anastassiou
    Pages 353-391

  4. High Order Approximation with Multivariate Generalized Gauss–Weierstrass Singular Integrals

    • George A. Anastassiou
    Pages 393-435

  5. Complete Approximations with Multivariate Generalized Poisson–Cauchy Type Singular Integral Operators

    • George A. Anastassiou
    Pages 437-478

  6. High Order Approximation with Multivariate Generalized Trigonometric Type Singular Integral Operators

    • George A. Anastassiou
    Pages 479-519

  7. Concluding Remarks

    • George A. Anastassiou
    Pages 521-522
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Keywords

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.

Authors and Affiliations

  • Department of Mathematical Sciences, University of Memphis, Memphis, USA

    George A. Anastassiou

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