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Boundary value problem for a fractional power of an elliptic operator isconsidered. An integral representation by means of a standard solution problemfor parabolic equations is used to solve such problems. Quadrature generalizedGauss-Laguerre formulas are constructed. We examine the effect of keyparameters on the accuracy of the approximate solution: the number of nodes ofthe quadrature and fractional power of the operator. Computational experimentswere performed to model two-dimensional problem with a fractional power of anelliptic operator.

Approximate representation of the solutions of fractional elliptical BVP through the solution of parabolic IVP