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Constructive Fractional Analysis with Applications

  • 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. Front Matter

    Pages i-xv
  2. General Fractional Landau Inequalities

    • George A. Anastassiou
    Pages 61-76
  3. Abstract Fractional Landau Inequalities

    • George A. Anastassiou
    Pages 77-94
  4. Generalized Canavati Fractional Landau Inequalities

    • George A. Anastassiou
    Pages 119-131
  5. Sequential Left Abstract Fractional Landau Inequalities

    • George A. Anastassiou
    Pages 133-153
  6. High Order Generalized Landau Inequalities

    • George A. Anastassiou
    Pages 219-233
  7. Landau’s Inequality for Semigroups

    • George A. Anastassiou
    Pages 299-307
  8. Fractional Variable Order Gronwall Inequality

    • George A. Anastassiou
    Pages 309-313

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

Bibliographic Information

Buy it now

Buying options

eBook USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access