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On Certain Integral Equations of Convolution Type with Bessel-Function Kernels
Published online by Cambridge University Press: 20 January 2009
Extract
In this paper we first obtain elementary solutions of the integral equations
and
Using these solutions we then define operators of fractional integration. These operators may be regarded as a generalisation of the operators of fractional integration introduced by Sneddon (1) as a modification of Erdé1yi–Kober operators. In fact Erdélyi–Kober–Sneddon operators may be obtained by multiplying both sides of the equations by α-1½β and considering the limiting case α→0. We employ these operators to find a generalisation of the Mellin transform.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 2 , December 1966 , pp. 111 - 116
- Copyright
- Copyright © Edinburgh Mathematical Society 1966
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