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Category: General Natural Science(13/13)




E-books | Detail

Title: The Theory of Fractional Calculus (Second Edition)

Author: Takahiro INOUE

Category: General Natural Science
Number of pages: 224
Size: A5

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

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Book Summary

This book presents the theory of fractional calculus formulated by an operator-based method. The differentiation operator in the classical calculus is extended to a general linear operator which satisfies Leibniz's rule. The key idea in this theory is to consider a sequence of functions produced by iterated applications of such a linear operator to a function which belongs to some specified function space. The fractional power of such a linear operator is defined by extending the integral representation of a function in this sequence by analytic continuation. This book covers various contents of the fractional calculus: the commutators, the function sequence called the lambda-sequence, the generating function of the lambda-sequence, the integral representation of the lambda-sequence, the extended function sequences and their integral representations, the discrete representation of the fractional differ-integration, the composition rule for composite functions, the generalized fractional integration by parts, the fractional calculus of variations, the fractional differ-integration of a composite function, the Laplace and Fourier transforms of the fractional differ-integration, the fractional calculus on the coset space, various special functions of complex order, and miscellaneous applications of the 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.