Geodesic
Boundary value problem for a linear system of equations with the partial derivatives of fractional order
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 295-311

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In the paper а boundary value problem for a linear 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 derivative, boundary value problem, fundamental solution, Wright's function of the matrix argument. 
@article{CHFMJ_2017_2_3_a3,
     author = {M. O. Mamchuev},
     title = {Boundary value problem for a linear system of equations with the partial derivatives of fractional order},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {295--311},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a3/}
}
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M. O. Mamchuev. Boundary value problem for a linear system of equations with the partial derivatives of fractional order. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 295-311. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a3/