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

Author

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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)

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.

Suggested Citation

  • Margus Lillemäe & Arvet Pedas & Mikk Vikerpuur, 2025. "Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations," Mathematics, MDPI, vol. 13(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2573-:d:1722604
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    References listed on IDEAS

    as
    1. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
    2. Kolk, Marek & Pedas, Arvet & Tamme, Enn, 2016. "Smoothing transformation and spline collocation for linear fractional boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 234-250.
    3. María Pilar Velasco & David Usero & Salvador Jiménez & Luis Vázquez & José Luis Vázquez-Poletti & Mina Mortazavi, 2020. "About Some Possible Implementations of the Fractional Calculus," Mathematics, MDPI, vol. 8(6), pages 1-22, June.
    4. Mingxu Yi & Kangwen Sun & Jun Huang & Lifeng Wang, 2013. "Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, December.
    5. Marina Popolizio, 2018. "Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions," Mathematics, MDPI, vol. 6(1), pages 1-13, January.
    6. Mingxu Yi & Kangwen Sun & Jun Huang & Lifeng Wang, 2013. "Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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