Naimark Problem for a Fractional Ordinary Differential Equation

L. Kh. Gadzova

Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 195-202.

Résumé

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.

Détail

Keywords: Gerasimov–Caputo fractional derivative, Naimark problem, fractional derivative, fractional equation, functional, Mittag-Leffler function.

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