Fractional Integrals and Potentials: 1st Edition (Hardback) book cover

Fractional Integrals and Potentials

1st Edition

By Boris Rubin

Chapman and Hall/CRC

424 pages

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Hardback: 9780582253414
pub: 1996-06-24
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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

Preface

Notation

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

Bibliography

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics