On a connection between the N-dimensional fractional Laplacian and 1-D fractional operators on lattices
[EN] We show the remarkable fact that the nonlocal property of the discrete N dimensional fractional Laplacian acting in the second variable of the lattice N x Z(N) can be exchanged with an equivalent memory corresponding to a power of a onedimensional operator that acts only on the first variable o...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/194825 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/194825 |
| Access Level: | acceso abierto |
| Palabra clave: | N-dimensional discrete fractional Laplacian Semidiscrete heat semigroup Discrete in time fractional order operator |
| Sumario: | [EN] We show the remarkable fact that the nonlocal property of the discrete N dimensional fractional Laplacian acting in the second variable of the lattice N x Z(N) can be exchanged with an equivalent memory corresponding to a power of a onedimensional operator that acts only on the first variable of the complete lattice Z x Z(N). This property allows to reduce the number of calculations and leads to more complete analytical solutions of mathematical models on lattices. The connection is established by showing that a first order equation in the first variable, and of fractional order alpha > 0 in the second, has the same solution as another of order 1/alpha in the first variable and integer order in the second. As a result, we provide for the first time the fundamental solution for the N-dimensional heat equation discrete in time and space. |
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