## OP-SF WEB

### Extract from OP-SF NET

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.

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