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Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations

  • Book
  • © 2018

Overview

Authors:
  1. George A. Anastassiou

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

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  • Includes recent original research on abstract fractional calculus, inequalities, and approximations
  • Presents the strong left and right calculus for Banach space valued functions
  • Offers a valuable resource for researchers and graduate students alike

Part of the book series: Studies in Computational Intelligence (SCI, volume 734)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. A Strong Left Fractional Calculus for Banach Space Valued Functions

    • George A. Anastassiou
    Pages 1-31

  3. Strong Right Abstract Fractional Calculus

    • George A. Anastassiou
    Pages 33-63

  4. Strong Mixed and Generalized Abstract Fractional Calculus

    • George A. Anastassiou
    Pages 65-86

  5. Foundations of General Fractional Analysis for Banach Space Valued Functions

    • George A. Anastassiou
    Pages 87-145

  6. Vector Abstract Fractional Korovkin Approximation

    • George A. Anastassiou
    Pages 147-173

  7. Basic Abstract Korovkin Theory

    • George A. Anastassiou
    Pages 175-188

  8. High Approximation for Banach Space Valued Functions

    • George A. Anastassiou
    Pages 189-210

  9. Vectorial Abstract Fractional Approximation Using Linear Operators

    • George A. Anastassiou
    Pages 211-233

  10. Abstract Fractional Trigonometric Korovkin Approximation

    • George A. Anastassiou
    Pages 235-259

  11. Multivariate Abstract Approximation for Banach Space Valued Functions

    • George A. Anastassiou
    Pages 261-281

  12. Arctangent Function Based Abstract Neural Network Approximation

    • George A. Anastassiou
    Pages 283-319
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Keywords

About this book

This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently.


This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.

Reviews

“In this brief monograph the author presents a strong theory of abstract fractional calculus for Banach–valued functions in which the integrals used to define the fractional derivatives are Bochner type integrals. His presentation includes left and right Caputo type and Canavati type fractional derivatives. … Each chapter is self-contained and can be read independently and, moreover, the monograph is suitable for the use in related graduate Classes.” (Mathematical Reviews, August, 2018)​

Authors and Affiliations

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

    George A. Anastassiou

Bibliographic Information

  • Book Title: Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations

  • Authors: George A. Anastassiou

  • Series Title: Studies in Computational Intelligence

  • DOI: https://doi.org/10.1007/978-3-319-66936-6

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG 2018

  • Hardcover ISBN: 978-3-319-66935-9Published: 12 September 2017

  • Softcover ISBN: 978-3-319-88349-6Published: 15 August 2018

  • eBook ISBN: 978-3-319-66936-6Published: 02 September 2017

  • Series ISSN: 1860-949X

  • Series E-ISSN: 1860-9503

  • Edition Number: 1

  • Number of Pages: X, 319

  • Topics: Computational Intelligence, Artificial Intelligence

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