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Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics

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 a...

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Detalles Bibliográficos
Autores principales: Mathai, A M, Haubold, H J
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-981-13-1159-8
http://cds.cern.ch/record/2638887
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author Mathai, A M
Haubold, H J
author_facet Mathai, A M
Haubold, H J
author_sort Mathai, A M
collection CERN
description 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.
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spelling cern-26388872021-04-21T18:43:09Zdoi:10.1007/978-981-13-1159-8http://cds.cern.ch/record/2638887engMathai, A MHaubold, H JErdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physicsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:26388872018
spellingShingle Mathematical Physics and Mathematics
Mathai, A M
Haubold, H J
Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
title Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
title_full Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
title_fullStr Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
title_full_unstemmed Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
title_short Erdélyi–Kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
title_sort erdélyi–kober fractional calculus: from a statistical perspective, inspired by solar neutrino physics
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-981-13-1159-8
http://cds.cern.ch/record/2638887
work_keys_str_mv AT mathaiam erdelyikoberfractionalcalculusfromastatisticalperspectiveinspiredbysolarneutrinophysics
AT hauboldhj erdelyikoberfractionalcalculusfromastatisticalperspectiveinspiredbysolarneutrinophysics