Bulavatsky V.M.
Fractional differential analog of biparabolic evolution equation and some its applications

The author analyzes fractional the differential analog of the well-known biparabolic evolution equation intended to describe the dynamics of heat and mass transfer processes that are non-equilibrium in time. Closed solution of some problems, in particular, the problem of Cauchy type and boundary-value problem for a finite interval, are obtained. A new (fractional differential) mathematical model is proposed to describe the non-equilibrium dynamics of filtration processes in fissured porous media. © 2016, Springer Science+Business Media New York.

Keywords: biparabolic evolution equation, boundary-value problem on a finite interval, fractional–differential analog, fundamental solution, mathematical modeling of the fractional–differential dynamics of filtration processes, nonclassical models, one-dimensional Cauchy-type problem, Boundary value problems, Dynamics, Mass transfer, Porous materials, Evolution equations, Filtration process, Finite intervals, Fundamental solutions, Nonclassical model, Differential equations

Cite:
Bulavatsky V.M. (2016). Fractional differential analog of biparabolic evolution equation and some its applications. Cybernetics and Systems Analysis, 52 (5), 89-100. doi: https://doi.org/10.1007/s10559-016-9875-5 http://jnas.nbuv.gov.ua/article/UJRN-0000553520 [In Russian].