Bulavatsky V.M., Bohaienko V.O.
Boundary-value problems for space-time fractional differential filtration dynamics in fractured-porous media

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 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, the authors 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 to the considered problems are given. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: and Riemann–Liouville derivatives, boundary-value problems, Caputo, closed-form solutions, fractional-differential dynamics of filtration processes, fractured-porous media, Hilfer, mathematical modeling, non-classical models, numerical solutions, Dynamics, Fracture, Inverse problems, Porous materials, And riemann–liouville derivative, Boundary-value problem, Caputo, Classical modeling, Closed form solutions, Filtration process, Fractional differential, Fractional-differential dynamic of filtration process, Fractured porous media, Hilfe, Mathematical modeling, Non-classical model, Numerical solution, Riemann-Liouville derivatives, Boundary value problems

Cite:
Bulavatsky V.M., Bohaienko V.O. (2022). Boundary-value problems for space-time fractional differential filtration dynamics in fractured-porous media. Cybernetics and Systems Analysis, 58 (3), 47–60. doi: https://doi.org/10.1007/s10559-022-00468-9 http://jnas.nbuv.gov.ua/article/UJRN-0001323856 [In Ukrainian].