【POD】The advanced theory of fractional calculus, 2nd Edition

Takahiro INOUE

2021年5月24日

学術研究出版

1,980円(税込)

科学・技術

Fractional calculus is an interpolation of differentiation and integration to fractional order. The study of fractional calculus has a long history over three centuries. Many famous mathematicians and theorists in science and engineering contributed to its development. The works on fractional calculus by Leibniz, Fourier, Abel, Liouville, Riemann, and Heaviside have been well-known. This book is a second edition of my monograph on the advanced theory of fractional calculus. In this book an integer power of an operator that satisfies Leibniz's rule is extended to complex order. And many classical formulae and theorems in differential and integral calculus are generalized to those of complex order. This book covers many interesting contents, such as an axiomatic formulation of a function space to which an operator is applied, an integral representation of a complex power of the operator, the linearity and continuity of a complex power of the operator, generalized Leibniz's theorem, the composition rule between complex powers of the operator, generalized fractional integration by parts, the basics of fractional calculus of variations, fractional differ-integration of composite functions, the Laplace and Fourier transforms in fractional calculus, an extended function space composed of distributions and its coset space, and special functions of complex order. In addition, miscellaneous problems in mathematics and physics are also illustrated as applications.

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