Geodesic
Boundary value problem for a multidinensional system of equations with Riemann--Liouvile fractional derivatives
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 732-747

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In the paper а 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. 
@article{SEMR_2019_16_a86,
     author = {M. O. Mamchuev},
     title = {Boundary value problem for a multidinensional system of equations with {Riemann--Liouvile} fractional derivatives},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {732--747},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a86/}
}
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M. O. Mamchuev. Boundary value problem for a multidinensional system of equations with Riemann--Liouvile fractional derivatives. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 732-747. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a86/