UDC 517.9: 519.6
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 v_bulav@ukr.net
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BOUNDARY-VALUE PROBLEMS OF FRACTIONAL-DIFFERENTIAL CONSOLIDATION
DYNAMICS FOR THE MODEL WITH THE CAPUTO–FABRIZIO DERIVATIVE
Abstract. Closed-form solutions to some boundary-value problems of fractional-differential filtration-consolidation dynamics with respect to the non-classical mathematical model taking into account the space-time nonlocality of the process are obtained. This mathematical model is formulated using the Caputo–Fabrizio derivative for the time variable and the Riemann-Liouville derivative for the geometric variable. Along with the direct consolidation problem for an array of finite thickness, the inverse boundary-value problems are considered to determine the unknown source functions that only depend on the geometric or time variable. Conditions for the existence of regular solutions to the considered problems are given.
Keywords: mathematical modeling, fractional-differential dynamics of consolidation processes, geoporous media, non-classical models, Caputo–Fabrizio and Riemann–Liouville derivatives, boundary-value problems, closed-form solutions, direct and inverse problems.
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