  In this paper we present a treatment of hypersingular integrals and integral
equations. It is shown the equivalence of different definitions of
hypersingular integrals. Then we construct explicit analytical solution to a
characteristic equation and prove convergence of the collocation method to this
solution. Further, we expand these results to full hypersingular kernels, and
give a demonstration of the developed method to some problems of crack
mechanics including crack problem for porous elastic materials, in the
framework of Cowin-Nunziato model.
