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.
