Download or read book Fractional Integrals and Potentials written by Boris Rubin and published by CRC Press. This book was released on 1996-06-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.