Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations

We consider an initial value problem for a system of linear fractional differential equations of Caputo type. Using an integral equation reformulation of the underlying problem, we first study the existence, uniqueness and smoothness of its exact solution. Based on the obtained results, a collocatio...

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Bibliographic Details
Published in:Mathematics
Main Authors: Margus Lillemäe, Arvet Pedas, Mikk Vikerpuur
Format: Article
Language:English
Published: MDPI AG 2025-08-01
Subjects:
system of fractional differential equations
Caputo fractional derivative
system of weakly singular integral equations
central part interpolation
collocation method
Online Access:https://www.mdpi.com/2227-7390/13/16/2573
Description
Summary:We consider an initial value problem for a system of linear fractional differential equations of Caputo type. Using an integral equation reformulation of the underlying problem, we first study the existence, uniqueness and smoothness of its exact solution. Based on the obtained results, a collocation-type method using the central part interpolation approach on the uniform grid is constructed and analyzed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.
ISSN:2227-7390

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