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Cauchy problems for second order hyperbolic differential equations with constant coefficients

Published online by Cambridge University Press:  20 January 2009

J. S. Lowndes
J. S. Lowndes
Affiliation:
Department of MathematicsUniversity of StrathclydeGlasgow, G1 1XH
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1. It is well known [1] that there is a one-to-one relation between solutions of the Darboux equation and the wave equation. The purpose of this paper is to show that some recent results in the fractional calculus can be used to obtain a similar connection between solutions of Darboux's equation and second order linear hyperbolic differential equations with constant coefficients.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 3 , October 1983 , pp. 307 - 311
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

1.Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 2 (Interscience, 1962).Google Scholar
2.Lowndes, J. S., An application of some fractional integrals, Glasgow Math. J. 20 (1979), 35–41.CrossRefGoogle Scholar
3.Lowndes, J. S., On some generalisations of the Riemann-Liouville and Weyl fractional integrals and their applications, Glasgow Math. J. 22 (1981), 173–180.CrossRefGoogle Scholar