Erdélyi–Kober Fractional Calculus
Title | Erdélyi–Kober Fractional Calculus PDF eBook |
Author | A. M. Mathai |
Publisher | Springer |
Pages | 132 |
Release | 2018-09-06 |
Genre | Science |
ISBN | 9811311595 |
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.
Recent Advances in Fractional Calculus
Title | Recent Advances in Fractional Calculus PDF eBook |
Author | R. N. Kalia |
Publisher | |
Pages | 332 |
Release | 1993 |
Genre | Mathematics |
ISBN |
Erdélyi-Kober Fractional Calculus
Title | Erdélyi-Kober Fractional Calculus PDF eBook |
Author | A. M. Mathai |
Publisher | |
Pages | 122 |
Release | 2018 |
Genre | Fractional calculus |
ISBN | 9789811311604 |
This book focuses on Erdelyi-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 Erdelyi-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.
Generalized Fractional Calculus and Applications
Title | Generalized Fractional Calculus and Applications PDF eBook |
Author | Virginia S Kiryakova |
Publisher | CRC Press |
Pages | 412 |
Release | 1993-12-27 |
Genre | Mathematics |
ISBN | 9780582219779 |
In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.
Fractional Calculus
Title | Fractional Calculus PDF eBook |
Author | Gary Francis Roach |
Publisher | Pitman Advanced Publishing Program |
Pages | 228 |
Release | 1985 |
Genre | Mathematics |
ISBN |
Fractional Calculus and Its Applications
Title | Fractional Calculus and Its Applications PDF eBook |
Author | B. Ross |
Publisher | Springer |
Pages | 391 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540699759 |
Fractional Differential Equations
Title | Fractional Differential Equations PDF eBook |
Author | Anatoly Kochubei |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 528 |
Release | 2019-02-19 |
Genre | Mathematics |
ISBN | 3110571668 |
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.