Fractional Integrals and Potentials  book cover
1st Edition

Fractional Integrals and Potentials

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ISBN 9780582253414
Published June 24, 1996 by Chapman and Hall/CRC
424 Pages

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Book Description

This volume presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. Beyond some basic properties of fractional integrals in one and many dimensions, it contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaudís approach and its generalization, leading to wavelet type representations.

Table of Contents

Chapter 1 Generalities
Chapter 2 One-dimensional fractional integrals
Chapter 3 Fractional integro-differentiation via wavelet transforms
Chapter 4 Riesz potentials on R
Chapter 5 Oscillatory potentials on R
Chapter 6 Potentials on a half-space
Chapter 7 Riesz potentials on a ball
Chapter 8 Fractional integrals on a sphere
Appendix 1
Appendix 2
Appendix 3

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