{"title":"Algorithms for the Numerical Solution of Fractional Differential Equations with Interval Parameters","authors":"A. Yu. Morozov, D. L. Reviznikov","doi":"10.1134/S1990478923040117","DOIUrl":null,"url":null,"abstract":"<p> The paper deals with the numerical solution of fractional differential equations with\ninterval parameters in terms of derivatives describing anomalous diffusion processes.\nComputational algorithms for solving initial–boundary value problems as well as the\ncorresponding inverse problems for equations containing interval fractional derivatives with\nrespect to time and space are presented. The algorithms are based on the previously developed\nand theoretically substantiated adaptive interpolation algorithm tested on a number of applied\nproblems for modeling dynamical systems with interval parameters; this makes it possible to\nexplicitly obtain parametric sets of states of dynamical systems. The efficiency and workability of\nthe proposed algorithms are demonstrated in several problems.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"815 - 827"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040117","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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