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Volume 13
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10.3390/math13162573
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Article

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

by
Margus Lillemäe
,
Arvet Pedas
* and
Mikk Vikerpuur
Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(16), 2573; https://doi.org/10.3390/math13162573
Submission received: 7 July 2025 / Revised: 2 August 2025 / Accepted: 11 August 2025 / Published: 12 August 2025
(This article belongs to the Section C1: Difference and Differential Equations)
Versions Notes

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 system of fractional differential equations; Caputo fractional derivative; system of weakly singular integral equations; central part interpolation; collocation method

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MDPI and ACS Style

Lillemäe, M.; Pedas, A.; Vikerpuur, M. Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations. Mathematics 2025, 13, 2573. https://doi.org/10.3390/math13162573

AMA Style

Lillemäe M, Pedas A, Vikerpuur M. Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations. Mathematics. 2025; 13(16):2573. https://doi.org/10.3390/math13162573

Chicago/Turabian Style

Lillemäe, Margus, Arvet Pedas, and Mikk Vikerpuur. 2025. "Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations" Mathematics 13, no. 16: 2573. https://doi.org/10.3390/math13162573

APA Style

Lillemäe, M., Pedas, A., & Vikerpuur, M. (2025). Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations. Mathematics, 13(16), 2573. https://doi.org/10.3390/math13162573

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