2019
Том 71
№ 1

All Issues

Basic boundary-value problems for one equation with fractional derivatives

Lopushanskaya G. P.

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Abstract

We prove some properties of solutions of an equation $\cfrac{\partial^{2\alpha}u}{\partial x_1^{2\alpha}} + \cfrac{\partial^{2\alpha}u}{\partial x_2^{2\alpha}} + \cfrac{\partial^{2\alpha}u}{\partial x_3^{2\alpha}} = 0, \quad \alpha \in \left( \cfrac 12\, ; 1 \right ]$, in a domain $\Omega \subset R^3$ which are similar to the properties of harmonic functions. By using the potential method, we investigate principal boundary-value problems for this equation.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 1, pp 51-65.

Citation Example: Lopushanskaya G. P. Basic boundary-value problems for one equation with fractional derivatives // Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 48–59.

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