E-books | Detail
Category: General Natural Science(11/11)

E-books | Detail

Title: The Theory of Fractional Calculus

Author: Takahiro INOUE

Category: General Natural Science
Number of pages: 210
Size: A5

e-Book compatible devices: pc
Viewer: ActiBook
Language: English



Book Summary

This book is a monograph on the theory of fractional calculus.
This is the rearranged and enhanced version of my previous books published under the titles "A Unified Theory of Generalized Differentiation and Integration" and "Fractional Calculus-A new approach from an operator-based formulation." This book covers comprehensive contents on the theory of the continuous fractional calculus from a viewpoint of function theory. In this book, the theory of fractional calculus is formulated by an operator-based method. A general operator satisfying Leibniz's rule is introduced instead of a differentiation operator in classical calculus. The function sequence generated by repeated applications of this operator to a function belonging to some well-defined function space plays an important role in constructing this theory. By extending the integral representation of an element of this function sequence, the complex power of this general operator is defined. This theory can be extended to a theory built on a coset space consisting of all the equivalence sets of generalized functions under the equivalence relation defined by the given general operator. In this theory, various special functions of non-negative integer degree are derived and are extended to complex degrees. Several interesting problems in mathematics and physics are treated by this theory to illustrate its applications. This book will benefit advanced students and researchers who are interested in fractional calculus.

Author Profile

Takahiro INOUE is a professor emeritus, Kumamoto University, a Doctor of Engineering, and a Fellow of IEICE (The Institute of Electronics, Information and Communication Engineers).
He has published 175 journal papers and 108 proceedings papers of international conferences. He is the author of Chapters 21 to 24 of "Electronic Circuit Handbook" published in 2006 by Asakura Publishing Co., Japan, the main author of the text book titled "Analog Electronic Circuits Learning by Examples" published in 2009 by Morikita Publishing Co., Japan, and the author of "A Unified Theory of Generalized Differentiation and Integration" and "Fractional Calculus" published in 2016 and 2018, respectively, by BookWay, Japan.