Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 685–695
Differentical equations, dynamical systems and optimal control
Boundary value problems for a linear ordinary differential equation of fractional order with delay
M. G. Mazhgikhova
Institute of Applied Mathematics and Automation,
Shortanova street, 89A,
360000, Nalchik, Russia
In this paper we obtained the explicit representations of the solutions of Dirichlet and Neumann problems for a linear ordinary differential equation of fractional order with delay. The Green's functions of the problems are constructed. The theorems of existence and uniqueness of solutions of investigated problems are proved. It is proved that the solvability conditions can be violated only a finite number of times.
differential equation of fractional order, differential equation with delay, the generalized Mittag-Leffler function, the generalized Wright function, the Green's function.
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Received November 9, 2017, published June 1, 2018
M. G. Mazhgikhova, “Boundary value problems for a linear ordinary differential equation of fractional order with delay”, Sib. Èlektron. Mat. Izv., 15 (2018), 685–695
Citation in format AMSBIB
\paper Boundary value problems for a linear ordinary differential equation of fractional order with delay
\jour Sib. \`Elektron. Mat. Izv.
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