UDC 517.9:519.6

Fractional differential analog of biparabolic evolution equation and some its applications

/ V.M. Bulavatsky // Kibernetika i sistemnyi analiz. — 2016. — Vol. 52, N 5. — P. 89–100.

The authors analyze the fractional differential analog of the well-known biparabolic evolution equation intended to describe the dynamics of heat and mass transfer processes in terms of their 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 filtrational processes in fractured porous media. Figs: 0. Tabl.: 0. Refs: 19 titles.

Keywords:

biparabolic evolution equation, fractional-differential analog, fundamental solution, Cauchy-type one-dimensional problem, boundary value problem on a finite interval, mathematical modeling of fractional-differential dynamics of filtration processes, non-classical models.


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Author(s):

Булавацкий Владимир Михайлович, профессор, доктор техн. наук, ведущий научный сотрудник Института кибернетики им. В.М. Глушкова НАН Украины, Киев,
e-mail: v_bulav@ukr.net