Basic boundary-value problems for one equation with fractional derivatives - Lopushanskaya, G. P. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We prove some properties of solutions of an equation $\cfrac{\partial^{2α}u}{\partial x_1^{2α}} + \cfrac{\partial^{2α}u}{\partial x_2^{2α}} + \cfrac{\partial^{2α}u}{\partial x_3^{2α}} = 0, \quad α \in \left( \cfrac 12\, ; 1 \right ]$,in a domain $Ω \subset R^3$ which are similar to the properties of harmonic functions. By using the potentialmethod, we investigate principal boundary-value problems for this equation.