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Unification of Fractional Calculi with Applications

  • Book
  • © 2022

Overview

Authors:
  1. George A. Anastassiou

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

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  • Presents applications in many areas of pure and applied mathematics
  • Specializes on fractional inequalities and fractional differential equations
  • Provides applications for applied sciences like geophysics, physics, chemistry, economics, and engineering

Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 398)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Progress on Generalized Hilfer Fractional Calculus and Fractional Integral Inequalities

    • George A. Anastassiou
    Pages 1-27

  3. Landau Generalized Hilfer Fractional Inequalities

    • George A. Anastassiou
    Pages 29-48

  4. Iyengar-Hilfer Generalized Fractional Inequalities

    • George A. Anastassiou
    Pages 49-90

  5. Generalized Hilfer-Polya, Hilfer-Ostrowski and Hilfer-Hilbert-Pachpatte Fractional Inequalities

    • George A. Anastassiou
    Pages 91-114

  6. Generalized Hilfer Fractional Approximation of Csiszar’s f-Divergence

    • George A. Anastassiou
    Pages 115-131

  7. Generalized Hilfer Fractional Self Adjoint Operator Inequalities

    • George A. Anastassiou
    Pages 133-155

  8. Essential Forward and Reverse Generalized Hilfer-Hardy Fractional Inequalities

    • George A. Anastassiou
    Pages 157-176

  9. Principles of Generalized Prabhakar-Hilfer Fractional Calculus and Applications

    • George A. Anastassiou
    Pages 177-196

  10. Advanced and General Hilfer-Prabhakar-Hardy Fractional Inequalities

    • George A. Anastassiou
    Pages 197-227

  11. Vectorial Advanced Hilfer-Prabhakar-Hardy Fractional Inequalities

    • George A. Anastassiou
    Pages 229-264

  12. Vectorial Prabhakar Hardy Advanced Fractional Inequalities Under Convexity

    • George A. Anastassiou
    Pages 265-306

  13. Advanced Multivariate Prabhakar fractional integrals and inequalities

    • George A. Anastassiou
    Pages 307-325

  14. Non Singular Kernel Multiparameter Fractional Differentiation

    • George A. Anastassiou
    Pages 327-340

  15. Advanced Hilfer Fractional Opial Inequalities

    • George A. Anastassiou
    Pages 341-363

  16. Exotic Fractional Integral Inequalities

    • George A. Anastassiou
    Pages 365-391

  17. Fuzzy Fractional Calculus

    • George A. Anastassiou
    Pages 393-417

  18. Conclusion

    • George A. Anastassiou
    Pages 419-419
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Keywords

About this book

This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners 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

  • Book Title: Unification of Fractional Calculi with Applications

  • Authors: George A. Anastassiou

  • Series Title: Studies in Systems, Decision and Control

  • DOI: https://doi.org/10.1007/978-3-030-86920-5

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-86919-9Published: 22 November 2021

  • Softcover ISBN: 978-3-030-86922-9Published: 23 November 2022

  • eBook ISBN: 978-3-030-86920-5Published: 21 November 2021

  • Series ISSN: 2198-4182

  • Series E-ISSN: 2198-4190

  • Edition Number: 1

  • Number of Pages: XI, 419

  • Topics: Engineering Mathematics, Complexity, Control and Systems Theory

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