THE REPRESENTATION PROBLEM FOR A DIFFUSION EQUATION AND FRACTAL R-L LADDER NETWORKS

Jacky Cresson; Anna Szafrańska

doi:10.30546/2409-4994.2024.50.1.115

THE REPRESENTATION PROBLEM FOR A DIFFUSION EQUATION AND FRACTAL R-L LADDER NETWORKS

Abstract

The representation problem is to prove that a discretization in space of the Fourier transform of a diffusion equation with a constant diffusion coefficient can be realized explicitly by an infinite fractal R-L ladder networks. We prove a rigidity theorem: a solution to the representation problem exists if and only if the space discretization is a geometric space scale and the fractal ladder networks is a Oustaloup one. In this case, the resistance and inertance of the ladder are explicitly determined up to a constant.

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Authors (2)

Jacky Cresson
- Univer- sité de Pau et des Pays de l’Adour-E2S
Anna Szafrańska dr inż.

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Keywords

FRACTAL R-L LADDER NETWORKS, FRACTIONAL BEHAVIOUR, DIFFUSION EQUATION, REPRESENTATION PROBLEM.

Details

Category:

Articles

Type:

artykuły w czasopismach

Published in:

Proceedings of the Institute of Mathematics and Mechanics no. 50, pages 115 - 125,
ISSN: 2409-4986

Language:

English

Publication year:

2024

Bibliographic description:

Szafrańska A., Cresson J.: THE REPRESENTATION PROBLEM FOR A DIFFUSION EQUATION AND FRACTAL R-L LADDER NETWORKS// Proceedings of the Institute of Mathematics and Mechanics -,iss. Vol. 50, nr 1 (2024), s.115-125

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