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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 685–695 (Mi semr945)  

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

Abstract: 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.

Keywords: differential equation of fractional order, differential equation with delay, the generalized Mittag-Leffler function, the generalized Wright function, the Green's function.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00462_


DOI: https://doi.org/10.17377/semi.2018.15.054

Full text: PDF file (162 kB)
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Document Type: Article
UDC: 517.91
MSC: 34L99
Received November 9, 2017, published June 1, 2018

Citation: 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
\Bibitem{Maz18}
\by M.~G.~Mazhgikhova
\paper Boundary value problems for a linear ordinary differential equation of fractional order with delay
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 685--695
\mathnet{http://mi.mathnet.ru/semr945}
\crossref{https://doi.org/10.17377/semi.2018.15.054}


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