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Intelligent Analysis: Fractional Inequalities and Approximations Expanded

  • Book
  • © 2020

Overview

Authors:
  1. George A. Anastassiou

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

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  • Presents recent research on Fractional Inequalities and Approximations Expanded
  • Original research presented in self-contained chapters which can be read independently
  • Provides a formal analysis on issues that are relevant decision making, complex processes, systems modeling and control, and related areas

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

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Table of contents (29 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. General Ordinary Iyengar Inequalities

    • George A. Anastassiou
    Pages 1-13

  3. Caputo Fractional Iyengar Inequalities

    • George A. Anastassiou
    Pages 15-28

  4. Canavati Fractional Iyengar Inequalities

    • George A. Anastassiou
    Pages 29-43

  5. General Multivariate Iyengar Inequalities

    • George A. Anastassiou
    Pages 45-66

  6. Multivariate Iyengar Inequalities for Radial Functions

    • George A. Anastassiou
    Pages 67-89

  7. Multidimensional Fractional Iyengar Inequalities for Radial Functions

    • George A. Anastassiou
    Pages 91-142

  8. General Multidimensional Fractional Iyengar Inequalities

    • George A. Anastassiou
    Pages 143-187

  9. Delta Time Scales Iyengar Inequalities

    • George A. Anastassiou
    Pages 189-212

  10. Time Scales Nabla Iyengar Inequalities

    • George A. Anastassiou
    Pages 213-239

  11. Choquet–Iyengar Advanced Inequalities

    • George A. Anastassiou
    Pages 241-256

  12. Fractional Conformable Iyengar Inequalities

    • George A. Anastassiou
    Pages 257-272

  13. Iyengar Fuzzy Inequalities

    • George A. Anastassiou
    Pages 273-282

  14. Choquet Integral Analytical Type Inequalities

    • George A. Anastassiou
    Pages 283-296

  15. Local Fractional Taylor Formula

    • George A. Anastassiou
    Pages 297-301

  16. Negative Domain Local Fractional Inequalities

    • George A. Anastassiou
    Pages 303-316

  17. Fractional Approximation by Riemann–Liouville Fractional Derivatives

    • George A. Anastassiou
    Pages 317-327

  18. Riemann–Liouville Fractional Fundamental Theorem of Calculus and Riemann–Liouville Fractional Polya Integral Inequality and the Generalization to Choquet Integral Case

    • George A. Anastassiou
    Pages 329-340

  19. Low Order Riemann–Liouville Fractional Inequalities with Absent Initial Conditions

    • George A. Anastassiou
    Pages 341-353

  20. Low Order Fractional Riemann–Liouville Inequalities on a Spherical Shell

    • George A. Anastassiou
    Pages 355-363
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Keywords

About this book

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.

Authors and Affiliations

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

    George A. Anastassiou

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