A boundary value problem on the semi-axis for an ordinary differential equation with a fractional Caputo derivative
https://doi.org/10.25587/SVFU.2023.49.50.003
Abstract
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.
About the Authors
I. E. Egorov
Ammosov North-Eastern Federal University, Scientific Research Institute of Mathematics
Russian Federation
Russian Federation
Ivan E. Egorov
58 Belinsky Street, Yakutsk 677891, Russia
E. D. Fedotov
Yakutsk Branch of the Regional Scientific and Educational Mathematical Center "Far Eastern Center of Mathematical Research"
Russian Federation
Russian Federation
Egor D. Fedotov
48 Kulakovsky Street, Yakutsk 677000, Russia
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Review
For citations:
Egorov I.E., Fedotov E.D. A boundary value problem on the semi-axis for an ordinary differential equation with a fractional Caputo derivative. Mathematical notes of NEFU. 2023;30(2):30-39. (In Russ.) https://doi.org/10.25587/SVFU.2023.49.50.003
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