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Diffusion problems on fractional nonlocal media

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Central European Journal of Physics

Abstract

In this paper, the nonlocal diffusion in one-dimensional continua is investigated by means of a fractional calculus approach. The problem is set on finite spatial domains and it is faced numerically by means of fractional finite differences, both for what concerns the transient and the steady-state regimes. Nonlinear deviations from classical solutions are observed. Furthermore, it is shown that fractional operators possess a clear physical-mechanical meaning, representing conductors, whose conductance decays as a power-law of the distance, connecting non-adjacent points of the body.

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Authors and Affiliations

  1. Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Alberto Sapora, Pietro Cornetti & Alberto Carpinteri

Authors
  1. Alberto Sapora
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  2. Pietro Cornetti
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  3. Alberto Carpinteri
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Correspondence to Alberto Sapora.

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Sapora, A., Cornetti, P. & Carpinteri, A. Diffusion problems on fractional nonlocal media. centr.eur.j.phys. 11, 1255–1261 (2013). https://doi.org/10.2478/s11534-013-0323-0

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  • DOI: https://doi.org/10.2478/s11534-013-0323-0

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