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

Natalia Dilna and Michal Fečkan
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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

Mathematics, 2022, vol. 10, issue 10, 1-15

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.

Keywords: fractional order functional differential equations; unique solvability; Caputo derivative; initial value problem; quasi-interior element; minihedral cone; pantograph-type model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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