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Title: Fractional Calculus (Third Edition): A New Approach from an Operator-Based Formulation

Author: Takahiro INOUE

Category: General Natural Science
Number of pages: 168
Size: A5

Notice: The e-book is available on Amazon Kindle Store.

Language: English

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Book Summary

This book is the third edition of my book published under the same title. In this third edition, theorems about the chain rule for differentiation of a composite function, fractional differ-integration of a composite function, and the Laplace transform of fractional differ-integration of a function are added to the previous editions. In this book, a theory of fractional calculus is formulated by an operator-based method. A general operator called the p-operator which satisfies Leibniz's rule is used instead of a differentiation operator in classical calculus. A function sequence generated by repeated applications of the p-operator to a function belonging to some specified function space plays an important role in constructing this theory. It is shown that this theory can be extended to a theory on a coset space consisting of the equivalence sets of generalized functions. Under this theory, various special functions of non-negative integer degree can be extended to complex degrees. Several typical 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.

From the Author