Geodesic
Boundary value problems for a linear ordinary differential equation of fractional order with delay
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 685-695.

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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. 
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M. G. Mazhgikhova. Boundary value problems for a linear ordinary differential equation of fractional order with delay. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 685-695. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a92/

[1] A.V. Pskhu, Partial differential equations of fractional order, Nauka, M., 2005 (Russian) | MR | Zbl

[2] J.H. Barrett, “Differential equation of non-integer order”, Canad. J. Math., 6:4 (1954), 529–541 | DOI | MR | Zbl

[3] M.M. Dzhrbashyan, A.B. Nersesyan, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”, Izv. Akad. Nauk Armenian SSR Matem., 3:1 (1968), 3–-29 (Russian) | MR | Zbl

[4] M.M. Dzhrbashyan, “Boundary problem for fractional differential operator of Sturm-Liouville type”, Izv. Akad. Nauk Armenian SSR Matem., 5:2 (1970), 71–96 (Russian) | Zbl

[5] A.V. Pskhu, “Initial-value problem for a linear ordinary differential equation of noninteger order”, Sb. Mathematics, 202:4 (2011), 571–-582 | DOI | MR | Zbl

[6] L.Kh. Gadzova, “Dirichlet and Neumann problems for a fractional ordinary differential equation with constant coefficients”, Differential Equations, 51:12 (2015), 1556–1562 | DOI | MR | Zbl

[7] S.B. Norkin, “About the solutions of a linear homogeneous second order differential equation with delay”, Uspekhi matem. nauk, 14:1(85) (1959), 199–206 (Russian) | MR | Zbl

[8] M.G. Mazhgikhova, “Initial and boundary value problem for ordinary differential equation of fractional order with delay”, Chelyabinsk Phisical and Mathematical Journal, 3:1 (2018), 27–37 (Russian)

[9] M.G. Mazhgikhova, “Dirichlet problem for ordinary differential equation of fractional order with delay”, Differential Equations, 54:2 (2015), 187–194 (Russian)

[10] M.G. Mazhgikhova, “Cauchy problem for ordinary differential equation with Riemann-Liouville derivative with delay”, News of kabardino-balkarian scientific center of the russian academy of sciences, 1:75 (2017), 24–28 (Russian)

[11] T.R. Prabhakar, “A singular integral equation with a generalized Mittag-Leffler function in the kernel”, Yokohama Math. J., 19 (1971), 7–15 | MR | Zbl

[12] A.K. Shukla, J.C. Prajapati, “On a generalization of Mittag-Leffler function and its properties”, J. Math. Anal. Appl., 336:2 (2007), 797–811 | DOI | MR | Zbl

[13] E.M. Wright, “The asymptotic expansion of the generalized hypergeometric function”, J. London Math. Soc., 10 (1935), 286–293 | DOI | MR | Zbl

[14] E.M. Wright, “The asymptotic expansion of the generalized hypergeometric function”, Proc. London Math. Soc., II Ser., 46 (1940), 389–408 | DOI | MR | Zbl