Abstract
The double Laplace transform is applied to the recently introduced fractional analogue of two-dimensional Laplace operator.
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Notes
- 1.
One of the reasons to consider the operator in skewed form, i.e. to have both derivatives in x and y in both terms, is to enrich the set of eigenfunctions of the operator.
- 2.
Similar definition with extra normalization was proposed in [DiPr65].
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Acknowledgements
The work is partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007–2013/ under REA grant agreement PIRSES-GA-2013-610547 - TAMER and by Belarusian Fund for Fundamental Scientific Research (grant F17MS-002).
The authors are grateful to an anonymous referee for attentive reading of the paper and making important remarks improving the presentation.
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Rogosin, S., Dubatovskaya, M. (2017). Double Laplace Transform and Explicit Fractional Analogue of 2D Laplacian. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_25
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