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A family of integral representations for the solution of the diffusion equation

Part of the Lecture Notes in Mathematics book series (LNM,volume 457)

Abstract

The problem here is to give a new derivation of a certain family of representations for the solution of the diffusion problem. The derivation of these representations are greatly facilitated by utilizing the techniques of fractional integration by parts.

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References

  1. Donaldson, J.A., "New Integral Representations for Solutions of Cauchy's Problem for Abstract Parabolic Equations," Proc. of the National Academy of Sciences, vol. 68 (1971), pp. 2025–2027.

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  2. Love, E.R. and Young, L.C., "On Fractional Integration by Parts," Proc. London Math. Society, ser. 2, vol. 44 (1938), pp. 1–35.

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  3. Widder, D.V., The Laplace Transform, Princeton University Press, 1941, pp. 70–75.

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© 1975 Springer-Verlag

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Donaldson, J.A. (1975). A family of integral representations for the solution of the diffusion equation. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067102

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  • DOI: https://doi.org/10.1007/BFb0067102

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

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