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

Margus Lillemäe, Arvet Pedas () and Mikk Vikerpuur
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Margus Lillemäe: Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia
Arvet Pedas: Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia
Mikk Vikerpuur: Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia

Mathematics, 2025, vol. 13, issue 16, 1-19

Abstract: 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.

Keywords: system of fractional differential equations; Caputo fractional derivative; system of weakly singular integral equations; central part interpolation; collocation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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