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Solvability of some Abel-type integral equations involving the Gauss hypergeometric function as kernels in the spaces of summable functions

Published online by Cambridge University Press:  17 February 2009

R. K. Raina ,
H. M. Srivastava ,
A. A. Kilbas  and
M. Saigo
R. K. Raina
Affiliation:
Department of Mathematics, College of Technology and Agricultural Engineering, Rajasthan Agricultural University, Udaipur 313001, Rajasthan, India. e-mail: raina_rk@yahoo.com
H. M. Srivastava
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada. e-mail: hmsri@uvvm.uvic.ca
A. A. Kilbas
Affiliation:
Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk, Belarus. e-mail: kilbas@mmf.bsu.unibel.by
M. Saigo
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan. e-mail: msaigo@fukuoka-u.ac.jp
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Abstract

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This paper is devoted to the study of the solvability of certain one-and multidimensional Abel-type integral equations involving the Gauss hypergeometric function as their kernels in the space of summable functions. The multidimensional equations are considered over certain pyramidal domains and the results obtained are used to present the multidimensional pyramidal analogues of generalized fractional calculus operators and their properties.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 2 , October 2001 , pp. 291 - 320
Copyright
Copyright © Australian Mathematical Society 2001

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