Topic #10 ------------- OP-SF NET 5.4 ------------ July 15, 1998 ~~~~~~~~~~~~~ From: Vadim Zelenkov
Subject: Book on Fractional Order Integral Transforms of Hypergeometric Type Fractional Order Integral Transforms of Hypergeometric Type By N. Virchenko and V. Tsarenko, Kiev, 1995, 216 pages, ISBN 5-7702-1101-6, in Russian This book deals with the theory and apparatus of new integral transforms (the fractional G-transforms) with kernels which are transcendental solutions of differential equations of hypergeometric type. Following this is a development and research in the theory of integral operators, integral equations with Gauss hypergeometric function which correspond to different special cases of parameters and variables. The main titles of the sections are as follows: Chapter 1. Integral transforms of the fractional order connected to orthogonal polynomials. 1. Some information on the theory of orthogonal polynomials. 2. Integral transforms of fractional order. 3. Basic fractional operational calculus. 4. Some applications of integral fractional G-calculus. Chapter 2. Integral transforms connected to the hypergeometric function _2F_1(a,b;c;z). 1. Application of classical methods for reception of the inversion formulae. 2. Method of fractional integro-differentiation.