^{1}Bogaenko, VA, ^{1}Bulavatsky, VM^{1}V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv |

Dopov. Nac. akad. nauk Ukr. 2018, 12:21-29 |

https://doi.org/10.15407/dopovidi2018.12.021 |

Section: Information Science and Cybernetics |

Language: Russian |

Abstract: The mathematical modeling of the fractional differential dynamics of the process of anomalous convective diffusion of soluble substances is conducted for the case of flat-vertical steady state groundwater filtration with free surface. Within the framework of the model with a generalized Caputo—Gerasimov fractional derivative, the corresponding non-linear boundary-value problem is posed, a finite-difference method for its approximated solution is given, and the results of computer experiments are described. |

Keywords: dynamics of convective and diffusive processes, finite-difference solutions, fractional differential mathematical models, generalized Caputo—Gerasimov derivative, mathematical and computer modeling, non-linear boundary-value problems, steady state flat-vertical groundwater filtration |

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