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Naimark Problem for a Fractional Ordinary Differential Equation

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Abstract

For a fractional ordinary differential equation, we consider a problem where the boundary conditions are given in the form of linear functionals. This permits covering a fairly broad class of linear local and nonlocal conditions. The fractional derivative is understood in the sense of Gerasimov–Caputo. A necessary and sufficient condition for the unique solvability of the problem is obtained. A representation of the solution via special functions is found. A theorem on the existence and uniqueness of the solution is proved.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation of Kabardin–Balkar Scientific Center of Russian Academy of Sciences, Nalchik, 360000, Russia

    L. Kh. Gadzova

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  1. L. Kh. Gadzova
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Correspondence to L. Kh. Gadzova.

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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 195–202 https://doi.org/10.4213/mzm14008.

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Gadzova, L.K. Naimark Problem for a Fractional Ordinary Differential Equation. Math Notes 114, 159–164 (2023). https://doi.org/10.1134/S0001434623070179

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  • DOI: https://doi.org/10.1134/S0001434623070179

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