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