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Fractional Calculus (Second Edition): A New Approach from an Operator-Based Formulation : Takahiro INOUE | BookWay書店 BookWay書店 外国語版





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タイトル: Fractional Calculus (Second Edition): A New Approach from an Operator-Based Formulation

著者: Takahiro INOUE  書店: BookWay書店 BookWay書店 外国語版 

カテゴリー: 自然科学一般
ページ数: 176
サイズ: A5

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本の要約

This book presents the theory of fractional calculus formulated by an operator-based method. The differentiation operator in classical fractional calculus is extended to a more general linear operator which satisfies Leibniz's rule. The key idea is to consider a sequence of functions produced by iterated applications of such a linear operator to a function belonging to some specified function space. Fractional power of such a linear operator is defined by extending the integral representation of a function in such a sequence by analytic continuation. The advantage of this theory is that it can grasp various special functions of arbitrary order within its scope and this scope is broad enough to induce a theory of fractional calculus on some coset space. In this book, miscellaneous problems in mathematics and physics are described as applications of the theory.

著者のプロフィール

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 2017, respectively, by BookWay, Japan.

著者からの書籍PR

This is the final version of a series of research books titled "a unified theory of generalized differentiation and integration"(1st to 3rd editions) and "fractional calculus"(1st edition) all of which are published through BookWay. Through these publications the contents are modified and improved to a stage broad enough to include a special function theory and a fractional calculus on some coset space. I believe that the proposed theory is sufficiently general and useful for solving problems in various fields in physics and engineering. Readers who are interested in mathematics of the proposed theory may enjoy remarks which point out important or interesting issues relating to theorems placed throughout this book.

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