Approximate solution of the integral equations involving kernel with additional singularity

The article is devoted to the approximate solutions of Fredholm integral equations second kind with weak singular kernel that can have additional singularity in numerator. We describe two problems lead such equations. They are problem minimization small deviations and entropy problem. Both them appear when considering a dynamical system involving mixed fractional Brownian motion. In order apply well-known numerical methods for weakly kernels, we build continuous approximation solution an equation containing by whose kernels singular, but numerator continuous. prove approximated tend original equation. demonstrate numerically how our work being applied specific