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Open AccessArticle

Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative

VM Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv 03680, Ukraine
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Fractal Fract 2018, 2(4), 28; https://doi.org/10.3390/fractalfract2040028
Received: 1 October 2018 / Revised: 20 October 2018 / Accepted: 23 October 2018 / Published: 24 October 2018
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
Within the framework of a new mathematical model of convective diffusion with the k-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corresponding filtration scheme, we consider the scheme for the spread of pollution from rivers, canals, or storages of industrial wastes. On the base of a locally one-dimensional finite-difference scheme, we develop a numerical method for obtaining solutions of boundary value problem for fractional differential equation with k-Caputo derivative with respect to the time variable that describes the convective diffusion of salt solution. The results of numerical experiments on modeling the dynamics of the considered process are presented. The results that show an existence of a time lag in the process of diffusion field formation are presented. View Full-Text
Keywords: groundwater filtration; convective diffusion; fractional differential model; k-Caputo derivative; finite-difference scheme groundwater filtration; convective diffusion; fractional differential model; k-Caputo derivative; finite-difference scheme
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Bohaienko, V.; Bulavatsky, V. Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative. Fractal Fract 2018, 2, 28.

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