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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 732–747 (Mi semr1091)

Differentical equations, dynamical systems and optimal control

Boundary value problem for a multidinensional system of equations with Riemann–Liouvile fractional derivatives

M. O. Mamchuev

Institute of Applied Mathematics and Automation of KBSC RAS, 89 A, Shortanov str., Nal'chik, 360000, Russia

Abstract: In the paper à boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann–Liouville sense with constant coefficients is studied in a rectangular domain. The existence and uniqueness theorem for the solution of the boundary value problem is proved. The solution is constructed in explicit form in terms of the Wright function of the matrix argument.

Keywords: system of partial differential equations, fractional derivatives, boundary value problem, fundamental solution, Wright's function of the matrix argument.

DOI: https://doi.org/10.33048/semi.2019.16.049

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UDC: 517.95
MSC: 35R11
Received March 26, 2018, published June 4, 2019

Citation: M. O. Mamchuev, “Boundary value problem for a multidinensional system of equations with Riemann–Liouvile fractional derivatives”, Sib. Èlektron. Mat. Izv., 16 (2019), 732–747

Citation in format AMSBIB
\Bibitem{Mam19} \by M.~O.~Mamchuev \paper Boundary value problem for a multidinensional system of equations with Riemann--Liouvile fractional derivatives \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 732--747 \mathnet{http://mi.mathnet.ru/semr1091} \crossref{https://doi.org/10.33048/semi.2019.16.049} `