Algorithms for the Numerical Solution of Fractional Differential Equations with Interval Parameters

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...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics Vol. 17; no. 4; pp. 815 - 827
Main Authors: Morozov, A. Yu, Reviznikov, D. L.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.09.2023
Springer Nature B.V
Subjects:
Adaptive algorithms
Algorithms
Approximation
Boundary conditions
Boundary value problems
Derivatives
Differential equations
Dynamical systems
Fractional calculus
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Parameters
Workability
inverse problem
parametric identification
interval parameter
fractional derivative
adaptive interpolation algorithm
anomalous diffusion
difference scheme
dynamical system
ISSN:1990-4789, 1990-4797
Online Access:Get full text
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Summary: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.
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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478923040117