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Basic boundary-value problems for one equation with fractional derivatives

Authors:

G P Lopushanskaya

Abstract:

We prove certain properties of solutions of the equation

$\frac{{\partial ^{2\alpha } u}}{{\partial x_1^{2\alpha } }} + \frac{{\partial ^{2\alpha } u}}{{\partial x_2^{2\alpha } }} + \frac{{\partial ^{2\alpha } u}}{{\partial x_3^{2\alpha } }} = 0,\alpha \in \left( {\frac{1}{2};1} \right]$

in a domain ω ⊂R ³, which are similar to the properties of harmonic functions. By using the potential method, we investigate basic boundary-value problems for this equation. Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 48–59, January, 1999.

Keywords:

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