Bulavatsky V.M.
Some boundary-value problems of filtration dynamics corresponding to fractional diffusion models of distributed order

On the basis of fractional diffusion models of distributed order, statements are made and closed-form solutions are obtained for some boundary-value problems of anomalous geofiltration dynamics, in particular, the problem of inflow to a gallery located between two supply lines in a three-layer geoporous medium. For a simplified version of the filtration model of distributed order, solutions are obtained for the direct and inverse boundary-value problems of filtration dynamics, as well as for the filtration problem with nonlocal boundary conditions. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary-value problem, closed-form solution, fractional–differential dynamics of filtration processes, geoporous media, mathematical modeling, model of filtration with distributed-order derivative, non-classical models, Boundary value problems, Filtration, Inverse problems, Porous materials, Boundary-value problem, Classical modeling, Closed form solutions, Filtration process, Fractional differential, Fractional–differential dynamic of filtration process, Geoporous medium, Mathematical modeling, Model of filtration with distributed-order derivative, Non-classical model, Dynamics

Cite:
Bulavatsky V.M. (2022). Some boundary-value problems of filtration dynamics corresponding to fractional diffusion models of distributed order. Cybernetics and Systems Analysis, 58 (1), 77–89. doi: https://doi.org/10.1007/s10559-022-00436-3 http://jnas.nbuv.gov.ua/article/UJRN-0001301508 [In Ukrainian].