This article is cited in 3 papers

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.

UDC: 517.91

MSC: 34L99

Received November 9, 2017, published June 1, 2018

DOI: 10.17377/semi.2018.15.054

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