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SpringerBriefs in Mathematical Physics

Erdélyi–Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

Authors: Mathai, A.M., Haubold, H.J.

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  • Is the first book to present a statistical perspective for Erdélyi–Kober operators of fractional calculus
  • Provides the interpretation of the diffusion entropy analysis of solar neutrino data of Super-Kamiokande in terms of anomalous diffusion
  • Explains the statistical perspective of Erdélyi–Kober fractional operators for anomalous reaction and diffusion processes dealt with in mathematical physics
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eBook $54.99
price for USA in USD (gross)
  • ISBN 978-981-13-1159-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-981-13-1158-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Solar Neutrinos, Diffusion, Entropy, Fractional Calculus

    Pages 1-12

    Mathai, A. M. (et al.)

  • Erdélyi-Kober Fractional Integrals in the Real Scalar Variable Case

    Pages 13-42

    Mathai, A. M. (et al.)

  • Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case

    Pages 43-72

    Mathai, A. M. (et al.)

  • Erdélyi-Kober Fractional Integrals in the Many Real Scalar Variables Case

    Pages 73-85

    Mathai, A. M. (et al.)

  • Erdélyi-Kober Fractional Integrals Involving Many Real Matrices

    Pages 87-98

    Mathai, A. M. (et al.)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-981-13-1159-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-981-13-1158-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Erdélyi–Kober Fractional Calculus
Book Subtitle
From a Statistical Perspective, Inspired by Solar Neutrino Physics
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
31
Copyright
2018
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-1159-8
DOI
10.1007/978-981-13-1159-8
Softcover ISBN
978-981-13-1158-1
Series ISSN
2197-1757
Edition Number
1
Number of Pages
XII, 122
Number of Illustrations
3 b/w illustrations, 3 illustrations in colour
Topics