Numerical solution of nonlinear Volterra integral equations with fractionally-exponential kernels of rheological models of viscoelastic continuum

This paper is devoted to numerical treatment of rheological models in the context of nonlinear heritable creep theory. An approximate method for nonlinear weakly singular Volterra integral equations with Rzhanitsyn's kernel used in rheological models of viscoelastic continuum is suggested. In conclusion we adduce some numerical results demonstrating the convergence of this method and describing the deformation of loamy soil.