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Exact Solvability Conditions for the Non-Local Initial Value Problem for Systems of Linear Fractional Functional Differential Equations

Author

Listed:
  • Natalia Dilna

    (Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

  • Michal Fečkan

    (Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
    Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská Dolina, 842 48 Bratislava, Slovakia)

Abstract

The exact conditions sufficient for the unique solvability of the initial value problem for a system of linear fractional functional differential equations determined by isotone operators are established. In a sense, the conditions obtained are optimal. The method of the test elements intended for the estimation of the spectral radius of a linear operator is used. The unique solution is presented by the Neumann’s series. All theoretical investigations are shown in the examples. A pantograph-type model from electrodynamics is studied.

Suggested Citation

  • Natalia Dilna & Michal Fečkan, 2022. "Exact Solvability Conditions for the Non-Local Initial Value Problem for Systems of Linear Fractional Functional Differential Equations," Mathematics, MDPI, vol. 10(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1759-:d:820692
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    References listed on IDEAS

    as
    1. Dilna, N. & Fečkan, M., 2018. "The Stieltjes string model with external load," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 350-359.
    2. Ahmed Alsaedi & Amjad F. Albideewi & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    3. Iskenderoglu, Gulistan & Kaya, Dogan, 2020. "Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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