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About this book :-
Erdélyi–Kober Fractional Calculus written by
A M Mathai, H J Haubold.
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.
Book Detail :-
Title: Erdélyi–Kober Fractional Calculus
Edition:
Author(s): A M Mathai, H J Haubold
Publisher: Springer Singapore
Series: SpringerBriefs in Mathematical Physics
Year: 2018
Pages: 132
Type: PDF
Language: English
ISBN: 978-981-13-1158-1;978-981-13-1159-8
Country: India
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About Author :-
Arak Mathai Arakaparampil Mathai "Arak" Mathai (born 1935) is an Indian mathematician who has worked in Statistics, Applied Analysis, Applications of special functions and Astrophysics. Mathai established the Centre for Mathematical Sciences, Palai, Kerala, India.
He has published more 25 books and more than 300 research publications. In 1998 he received the Founder Recognition Award from the Statistical Society of Canada. He is a Fellow of the National Academy of Sciences, India and a Fellow of the Institute of Mathematical Statistics. After completing his high school education in 1953 from St. Thomas High School, Palai with record marks he joined St. Thomas College, Palai and obtained his B Sc. degree in Mathematics in 1957. In 1959 he completed his master's degree in Statistics from University of Kerala, Thiruvananthapuram, Kerala, India with first class, first rank and gold medal. Then he joined St. Thomas College, Palai, University of Kerala, as a lecturer in Statistics and served there till 1961. He obtained Canadian Commonwealth scholarship in 1961 and went to University of Toronto, Canada for completing his MA degree in Mathematics in 1962. He was awarded PhD from University of Toronto, Canada in 1964. Then he joined McGill University, Canada as an Assistant Professor till 1968. From 1968 to 1978 he was an Associate Professor there. He became a Full Professor of McGill in 1979 and served the Department of Mathematics and Statistics until 2000. From 2000 onwards he was an Emeritus Professor of McGill University.
All Famous Books of this Author :-
Here is list all books/editions avaliable of this author, We recomended you to download all.
• Download PDF Linear Algebra: A Course for Physicists and Engineers by Arak Mathai, H J Haubold
• Download PDF Jacobians of Matrix Transformations and Functions of Matrix Argument by A M Mathai
• Download PDF Quadratic Forms in Random Variables by A M Mathai, S B Provost
• Download PDF Probability and Statistics: A Course for Physicists and Engineers by A M Mathai, H J Haubold
• Download PDF Probability and Statistics by Arak Mathai, P N Rathie
• Download PDF Erdélyi–Kober Fractional Calculus by A M Mathai, H J Haubold
• Download PDF Fractional & Multivariable Calculus by A M Mathai, H J Haubold
• Download PDF Fractional & Multivariable Calculus by A M Mathai, H J Haubold
• Download PDF Generalized Hypergeometric Functions by A M Mathai, R K Saxena
• Download PDF Special Functions for Applied Scientists by A M Mathai, H J Haubold
• Download PDF The H-Function: Theory and Applications by A M Mathai, Ram Kishore Saxena, Hans J Haubold
Book Contents :-
Erdélyi–Kober Fractional Calculus written by
A M Mathai, H J Haubold
cover the following topics.
1. Solar Neutrinos, Diffusion, Entropy, Fractional Calculus
2. Erdélyi-Kober Fractional Integrals in the Real Scalar Variable Case
3. Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case
4. Erdélyi-Kober Fractional Integrals in the Many Real Scalar Variables Case
5. Erdélyi-Kober Fractional Integrals Involving Many Real Matrices
6. Erdélyi-Kober Fractional Integrals in the Complex Domain
References
Index
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