Bulavatsky V.M.
Boundary-value problems of fractional-differential consolidation dynamics for the model with the Caputo–Fabrizio derivative

Closed-form solutions are obtained 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. 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 a soil mass 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. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary-value problems, Caputo–Fabrizio and Riemann–Liouville derivatives, closed-form solutions, direct and inverse problems, fractional-differential dynamics of consolidation processes, geoporous media, mathematical modeling, non-classical models, Dynamics, Inverse problems, Boundary-value problem, Caputo–fabrizio and riemann–liouville derivative, Classical modeling, Closed form solutions, Consolidation process, Direct and inverse problems, Fractional differential, Fractional-differential dynamic of consolidation process, Geoporous medium, Mathematical modeling, Non-classical model, Riemann-Liouville derivatives, Boundary value problems

Cite:
Bulavatsky V.M. (2023). Boundary-value problems of fractional-differential consolidation dynamics for the model with the Caputo–Fabrizio derivative. Cybernetics and Systems Analysis, 59 (4), 159–168. doi: https://doi.org/10.1007/s10559-023-00600-3 http://jnas.nbuv.gov.ua/article/UJRN-0001415733 [In Ukrainian].