A boundary value problem on the semi-axis for an ordinary differential equation with a fractional Caputo derivative. (Russian. English summary) Zbl 1536.34029
Summary: The paper considers the unique solvability of a boundary value problem on the semiaxis for a higher-order ordinary differential equation with a fractional Caputo derivative and constant coefficients in the class of bounded functions, where the order of the fractional Caputo derivative lies in the interval \((0, 1)\). Higher orders of the fractional derivative are obtained by composing fractional Caputo derivatives. A special case of the fractional Caputo derivative for integer orders of the derivative coincides with the classical concept of the derivative and the problem under consideration becomes a classical boundary value problem on the half-axis for a higher-order ordinary differential equation. For the equation under consideration, a fundamental system of solutions in the class of bounded functions is constructed. Conditions of the Lopatinsky type for boundary operators are obtained under which the boundary value problem is uniquely solvable in the class of bounded functions.
MSC:
| 34B40 | Boundary value problems on infinite intervals for ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
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| [23] | Поступила в редакцию 15 февраля 2022 г. После доработки 2 мая 2023 г. Принята к публикации 29 мая 2023 г. |
| [24] | Егоров Иван Егорович Научно-исследовательский институт математики СВФУ, ул. Кулаковского, 48, Якутск 677000 ivanegorov51@mail.ru Федотов Егор Дмитриевич Якутское отделение Регионального научно-образовательного математического центра Дальневосточный центр математических исследований ул. Белинского, 58, Якутск 677891 |
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