Erdélyi–Kober Fractional Calculus: From a Statistical Perspective, Inspired by Solar Neutrino Physics

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. Front Matter ....Pages i-xii Solar Neutrinos, Diffusion, Entropy, Fractional Calculus (A. M. Mathai, H. J. Haubold)....Pages 1-12 Erdélyi-Kober Fractional Integrals in the Real Scalar Variable Case (A. M. Mathai, H. J. Haubold)....Pages 13-42 Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case (A. M. Mathai, H. J. Haubold)....Pages 43-72 Erdélyi-Kober Fractional Integrals in the Many Real Scalar Variables Case (A. M. Mathai, H. J. Haubold)....Pages 73-85 Erdélyi-Kober Fractional Integrals Involving Many Real Matrices (A. M. Mathai, H. J. Haubold)....Pages 87-98 Erdélyi-Kober Fractional Integrals in the Complex Domain (A. M. Mathai, H. J. Haubold)....Pages 99-119 Back Matter ....Pages 121-122