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Title: The Theory of Fractional Calculus (Third Edition)

Author: Takahiro INOUE

Category: General Natural Science
Number of pages: 230
Size: A5

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

Language: English

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Book Summary

This book is a monograph on the theory of fractional calculus formulated by an operator-based method. The differential operator in the classical fractional calculus is extended to a general linear operator which satisfies Leibniz's rule. The key idea in this theory is a function sequence produced by iterated applications of such a linear operator to a function in some well-defined function space. This book covers various contents of the fractional calculus such as the commutators, the function sequence called the lambda-sequence in this book, the generating function of the lambda-sequence, the integral representation of the lambda-sequence, the discrete representation of the fractional differ-integration, the composition rule between an integer power and a complex power of (d/dx), the generalized fractional integration by parts, the basics of the fractional calculus of variations, the fractional differ-integration of composite functions, the Laplace and Fourier transforms of the fractional differ-integration, the extended function space composed of distributions, the fractional calculus on the coset space, the lambda-sequence in such an extended function space and its integral representation, and the derivation of special functions of complex order. Miscellaneous problems in mathematics and physics are also illustrated as applications of this theory.

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