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On Certain Integral Equations of Convolution Type with Bessel-Function Kernels

Published online by Cambridge University Press:  20 January 2009

R. P. Srivastav
R. P. Srivastav
Affiliation:
Department of Mathematics, Duke University, Durham, N.C.
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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

References

REFERENCES

(1) Sneddon, I. N., Fractional Integration and Dual Integral Equations, North Carolina State College Applied Mathematics Research Group, Report PSR-6 (1962).CrossRefGoogle Scholar
(2) Burlak, J., A pair of dual integral equations occurring in diffraction theory, Proc. Edinburgh Math. Soc. 13 (1962), 179–187.CrossRefGoogle Scholar
(3) Erdélyi, A. et al. , Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953).Google Scholar
(4) Erdélyi, A. et al. , Tables of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954).Google Scholar
(5) Erdélyi, A. et al. , Tables of Integral Transforms, Vol. 2 (McGraw-Hill, New York, 1954).Google Scholar