Bulavatsky V.M.
Mathematical models and problems of fractional-differential dynamics of some relaxational filtrational processes

The author constructs fractional-differential mathematical models to describe the dynamics of geofiltration processes under pressure relaxation. The models are based on the concepts of the generalized Caputo and Hilfer derivatives, as fractional-order derivatives of a function with respect to another function. Within the framework of these models, analytical solutions of some filtration boundary-value problems, including the problem with nonlocal boundary conditions, are obtained. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary-value problems, Caputo and Hilfer derivatives, fractional-differential mathematical models, locally non-equilibrium processes of geofiltration, mathematical modeling, nonlocal boundary conditions, Boundary conditions, Boundary value problems, Mathematical models, Filtration process, Fractional differential, Fractional order derivatives, Geofiltration, Non-local boundary conditions, Pressure relaxation, Filtration

Cite:
Bulavatsky V.M. (2018). Mathematical models and problems of fractional-differential dynamics of some relaxational filtrational processes. Cybernetics and Systems Analysis, 54 (5), 51-60. doi: https://doi.org/10.1007/s10559-018-0074-4 http://jnas.nbuv.gov.ua/article/UJRN-0000897815 [In Russian].