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Intelligent Analysis: Fractional Inequalities and Approximations Expanded

  • George A. Anastassiou
Book

Part of the Studies in Computational Intelligence book series (SCI, volume 886)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. George A. Anastassiou
    Pages 1-13
  3. George A. Anastassiou
    Pages 15-28
  4. George A. Anastassiou
    Pages 29-43
  5. George A. Anastassiou
    Pages 45-66
  6. George A. Anastassiou
    Pages 67-89
  7. George A. Anastassiou
    Pages 143-187
  8. George A. Anastassiou
    Pages 189-212
  9. George A. Anastassiou
    Pages 213-239
  10. George A. Anastassiou
    Pages 241-256
  11. George A. Anastassiou
    Pages 257-272
  12. George A. Anastassiou
    Pages 273-282
  13. George A. Anastassiou
    Pages 283-296
  14. George A. Anastassiou
    Pages 297-301
  15. George A. Anastassiou
    Pages 303-316
  16. George A. Anastassiou
    Pages 365-380
  17. George A. Anastassiou
    Pages 381-391
  18. George A. Anastassiou
    Pages 393-399
  19. George A. Anastassiou
    Pages 501-510
  20. George A. Anastassiou
    Pages 511-520
  21. George A. Anastassiou
    Pages 521-525

About this book

Introduction

This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.

Keywords

Computational and Fractional Analysis Choquet Integral Analytical Inequalities Iyengar Type Inequalities Local Fractional Taylor Formula Quantitative Complex Approximation Theory Csiszar’s Fdivergence Complex Multivariate Taylor Formula

Authors and affiliations

  • George A. Anastassiou
    • 1
  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-38636-8
  • Copyright Information The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Intelligent Technologies and Robotics
  • Print ISBN 978-3-030-38635-1
  • Online ISBN 978-3-030-38636-8
  • Series Print ISSN 1860-949X
  • Series Online ISSN 1860-9503
  • Buy this book on publisher's site