NAYMARK PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION WITH A FRACTIONAL DISCRETE DISTRIBUTED DIFFERENTIATION OPERATOR

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Abstract

For an ordinary differential equation with a fractional discretely distributed differentiation operator, the Naimark problem is studied, where the boundary conditions are specified in the form of linear functionals. This allows us to cover a fairly wide class of linear local and nonlocal conditions. A necessary and sufficient condition for the unique solvability of the problem is obtained. A representation of the solution to the problem under study is found in terms of special functions. The theorem of existence and uniqueness of the solution is proven.

About the authors

L. Kh Gadzova

Kabardin-Balkar Scientific Center of RAS

Email: macaneeva@mail.ru
Nalchik, Russia

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