Geodesic
Dirichlet problem for fractional differential equation with constant coefficients
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 4, pp. 401-411

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The Dirichlet problem is investigated for the ordinary differential equation with the Dzrbashyan and Nersesyan fractional differentiation operators. The solution is found in explicit form in terms of the Wright function. The existence and uniqueness solution theorem is proved. The Green function of the considered problem is constructed.
Keywords: Dirichlet problem, ordinary differential equation, fractional differentiation, Dzhrbashyan and Neresyan operator, Green's function. 
@article{CHFMJ_2017_2_4_a2,
     author = {F.T. Bogatyreva},
     title = {Dirichlet problem for fractional differential equation with constant coefficients},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {401--411},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a2/}
}
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F.T. Bogatyreva. Dirichlet problem for fractional differential equation with constant coefficients. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 4, pp. 401-411. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a2/