  Boundary value problem for a fractional power of an elliptic operator is
considered. An integral representation by means of a standard solution problem
for parabolic equations is used to solve such problems. Quadrature generalized
Gauss-Laguerre formulas are constructed. We examine the effect of key
parameters on the accuracy of the approximate solution: the number of nodes of
the quadrature and fractional power of the operator. Computational experiments
were performed to model two-dimensional problem with a fractional power of an
elliptic operator.

Numerical Analysis;Numerical Analysis