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UDC 517.9: 519.6
V.M. Bulavatsky1, V.O. Bohaienko2


1 V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine,
Kyiv, Ukraine

 v_bulav@ukr.net

2 V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine,
Kyiv, Ukraine

 sevab@ukr.net

BOUNDARY-VALUE PROBLEMS FOR SPACE-TIME FRACTIONAL DIFFERENTIAL
FILTRATION DYNAMICS IN FRACTURED-POROUS MEDIA

Abstract. Closed-form solutions are obtained for some non-stationary boundary-value problems of filtration dynamics in fractured-porous formations, posed within the framework of fractional-differential mathematical models, taking into account the space-time nonlocality of the process. The indicated mathematical models of anomalous filtration dynamics are formulated using the Hilfer or Caputo derivatives with respect to the time variable and the Riemann–Liouville derivative with respect to the geometric variable. Along with direct filtration problems, we also consider the inverse boundary-value problem of determining the unknown source function that depends only on the geometric variable. Conditions of the existence of regular solutions for the considered problems are given .

Keywords: mathematical modeling, fractional-differential dynamics of filtration processes, fractured-porous media, non-classical models, Hilfer, Caputo, and Riemann–Liouville derivatives, boundary value problems, closed-form solutions, numerical solutions.


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