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Erdélyi–Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

  • A. M. Mathai
  • H. J. Haubold

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 31)

Table of contents

  1. Front Matter
    Pages i-xii
  2. A. M. Mathai, H. J. Haubold
    Pages 1-12
  3. A. M. Mathai, H. J. Haubold
    Pages 99-119
  4. Back Matter
    Pages 121-122

About this book

Introduction

This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdélyi–Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics.

A major mathematical objective of this book is specifically to examine a new definition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a definition for the case of real-valued scalar functions of several matrices.

Keywords

Fractional calculus Fractional operators Real variable case Multivariable case Matrix-variate case

Authors and affiliations

  • A. M. Mathai
    • 1
  • H. J. Haubold
    • 2
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.Office for Outer Space Affairs United NationsViennaAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-1159-8
  • Copyright Information The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-13-1158-1
  • Online ISBN 978-981-13-1159-8
  • Series Print ISSN 2197-1757
  • Series Online ISSN 2197-1765
  • Buy this book on publisher's site
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