Geodesic
Algorithms for the numerical solution of fractional differential equations with interval parameters
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 93-108

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The paper deals with the numerical solution of fractional differential equations with interval parameters in terms of derivatives describing anomalous diffusion processes. Computational algorithms for solving initial-boundary value problems as well as the corresponding inverse problems for equations containing interval fractional derivatives with respect to time and space are presented. The algorithms are based on the previously developed and theoretically substantiated adaptive interpolation algorithm tested on a number of applied problems for modeling dynamical systems with interval parameters; this makes it possible to explicitly obtain parametric sets of states of dynamical systems. The efficiency and workability of the proposed algorithms are demonstrated in several problems.
Keywords: fractional derivative, difference scheme, inverse problem, parametric identification, interval parameter, dynamical system
Mots-clés : anomalous diffusion, adaptive interpolation algorithm. 
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     author = {A. Yu. Morozov and D. L. Reviznikov},
     title = {Algorithms for the numerical solution of fractional differential equations with interval parameters},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {93--108},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a6/}
}
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A. Yu. Morozov; D. L. Reviznikov. Algorithms for the numerical solution of fractional differential equations with interval parameters. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 93-108. http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a6/