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Modelling Fractional Advection–Diffusion Processes via the Adomian Decomposition

Author

Listed:
  • Alberto Antonini

    (Department of Civil, Environmental and Architectural Engineering, University of Padua, Via F. Marzolo 9, 35131 Padova, Italy)

  • Valentina Anna Lia Salomoni

    (Department of Civil, Environmental and Architectural Engineering, University of Padua, Via F. Marzolo 9, 35131 Padova, Italy
    Department of Management and Engineering, University of Padua, Stradella S. Nicola 3, 36100 Vicenza, Italy)

Abstract

When treating geomaterials, fractional derivatives are used to model anomalous dispersion or diffusion phenomena that occur when the mass transport media are anisotropic, which is generally the case. Taking into account anomalous diffusion processes, a revised Fick’s diffusion law is to be considered, where the fractional derivative order physically reflects the heterogeneity of the soil medium in which the diffusion phenomena take place. The solutions of fractional partial differential equations can be computed by using the so-called semi-analytical methods that do not require any discretization and linearization in order to obtain accurate results, e.g., the Adomian Decomposition Method (ADM). Such a method is innovatively applied for overcoming the critical issue of geometric nonlinearities in coupled saturated porous media and the potentialities of the approach are studied, as well as findings discussed.

Suggested Citation

  • Alberto Antonini & Valentina Anna Lia Salomoni, 2023. "Modelling Fractional Advection–Diffusion Processes via the Adomian Decomposition," Mathematics, MDPI, vol. 11(12), pages 1-30, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2657-:d:1168449
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    References listed on IDEAS

    as
    1. S. Saha Ray & R. K. Bera, 2004. "Solution of an extraordinary differential equation by Adomian decomposition method," Journal of Applied Mathematics, Hindawi, vol. 2004, pages 1-8, January.
    2. Hassan Khan & Rasool Shah & Poom Kumam & Dumitru Baleanu & Muhammad Arif, 2019. "An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    3. Salah Abuasad & Ishak Hashim & Samsul Ariffin Abdul Karim, 2019. "Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-14, May.
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