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Basic boundary-value problems for one equation with fractional derivatives

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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.

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Authors
  1. G. P. Lopushanskaya
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Additional information

Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 48–59, January, 1999.

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Lopushanskaya, G.P. Basic boundary-value problems for one equation with fractional derivatives. Ukr Math J 51, 51–65 (1999). https://doi.org/10.1007/BF02591914

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  • DOI: https://doi.org/10.1007/BF02591914

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