Method of variational interpolation in inverse problems of anomalous diffusion of fractional-differential type

V. A. Litvinov^a, V. V. Uchaikin<sup>b

a</sup> Barnaul Law Institute of the Ministry of Internal Affairs of Russia, Barnaul, Russia
^b Lev Tolstoi Ulyanovsk State University, Ulyanovsk, Russia

Abstract: The work considers problem of reconstruction of differential equations parameters, describing anomalous diffusion processes, on the base of known solutions. As a tool, is used the variational interpolation method elaborated by the authors earlier. The reconstruction time-dependence of diffusivity and determination of fractional time- and space-derivatives order in anomalous diffusion equation is demonstrated. There is shown a possibility of sufficient accuracy with insignificant computational expanses.

Key words: inverse problems, diffusion equation, operators, fractional derivatives.

UDC: 517.97

Received: 14.03.2019
Revised: 17.09.2020
Accepted: 14.07.2021

DOI: 10.15372/SJNM20210404

 English version: Numerical Analysis and Applications, 2021, 14:4, 343–356

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