Solution of boundary-value problems of linear viscoelasticity by the method of operator continued fractions in the case of complex coefficients

The case is considered where complex coefficients of operators appear when irrational functions of integral resolvent operators of viscoelasticity are approximated by continued fractions. Approximating formulas in explicit form are derived for this case. The relations obtained, are applied to the solution of the problem on time redistribution of stresses in a viscoelastic transversal-isotropic hyperboloid.