Geodesic
Method of variational interpolation in inverse problems of anomalous diffusion of fractional-differential type
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 4, pp. 393-408

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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. 
@article{SJVM_2021_24_4_a4,
     author = {V. A. Litvinov and V. V. Uchaikin},
     title = {Method of variational interpolation in inverse problems of anomalous diffusion of fractional-differential type},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {393--408},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a4/}
}
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V. A. Litvinov; V. V. Uchaikin. Method of variational interpolation in inverse problems of anomalous diffusion of fractional-differential type. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 4, pp. 393-408. http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a4/