Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies - Sinaiskii, E. S. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We consider a boundary-value problem of mechanics of inhomogeneous hereditarily elastic bodies formulated as a linear equation with an operator of fractional integration, partial derivatives with respect to time and spatial variables, and polynomial-type coefficients of one of the variables. An approximate solution of this problem is constructed according to Dzyadyk's a-method combined with the use of the Laplace transformation. It is proved that the errors of the approximation of the required function and its derivatives decrease in geometric progression.