Geodesic
The Dirichlet problem for the generalized Laplace equation with fractional derivative
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 312-322

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In the paper the Dirichlet problem for the generalized Laplace equation with fractional Riemann — Liouville derivative with respect to one of the two independent variables in the upper half-plane is investigated. The representation of the solution is found by the method of integral transformation with the Wright function in the core and the uniqueness theorem for the solution of the problem is proved by the method abc.
Keywords: Riemann — Liouville fractional derivative, Wright function, generalized Laplace equation with fractional derivative, Dirichlet boundary value problem. 
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     author = {O. Kh. Masaeva},
     title = {The {Dirichlet} problem for the generalized {Laplace} equation with fractional derivative},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {312--322},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a4/}
}
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O. Kh. Masaeva. The Dirichlet problem for the generalized Laplace equation with fractional derivative. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 312-322. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a4/