Authors:
- 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
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 31)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
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.Authors and Affiliations
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Department of Mathematics and Statistics, McGill University, Montreal, Canada
A. M. Mathai
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Office for Outer Space Affairs United Nations, Vienna, Austria
H. J. Haubold
Bibliographic Information
Book Title: Erdélyi–Kober Fractional Calculus
Book Subtitle: From a Statistical Perspective, Inspired by Solar Neutrino Physics
Authors: A. M. Mathai, H. J. Haubold
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-981-13-1159-8
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018
Softcover ISBN: 978-981-13-1158-1Published: 17 September 2018
eBook ISBN: 978-981-13-1159-8Published: 06 September 2018
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: XII, 122
Number of Illustrations: 3 b/w illustrations, 3 illustrations in colour
Topics: Mathematical Physics, Special Functions, Functional Analysis