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Fractional Calculus An Extension of Differential and Integral Calculus

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Fractional Calculus An Extension of Differential and Integral Calculus

著者:
Takahiro Inoue
出版社:
学術研究出版

概要:

This book is a monograph on an extension of differential and integral calculus. The theory in this book is built on an operator-theoretic formulation of fractional calculus. An integer power of a linear operator satisfying Leibniz's rule is extended to a complex power and many formulas with integer powers of such an operator in differential and integral calculus are extended into a domain of complex powers. Such extensions include, for example, Leibniz's theorem, composition rules of operators, integration by parts, the calculus of variations, the Laplace transform, the Fourier transform, and various kinds of special functions including the Bessel polynomial introduced by Krall and Frink. Faà di Bruno's formula on differentiation of a composite function is also extended to a more general operator-based formula. In the last chapter of this book, miscellaneous problems in mathematics, physics, and engineering are illustrated as applications. The reader of this book is assumed to be acquainted with undergraduate-level complex analysis together with a bit of knowledge of function theory, topology, and abstract algebra.

ジャンル:
理学・工学 > 数学
販売開始:
2022/09/29
ページ数
252ページ
ファイルサイズ:
90.87MB
CODE:
J0010380BK0130870001
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Fractional Calculus An Extension of Differential and Integral Calculus
販売(無期限): ¥ 1,870(税込)