  We give the regularization for fractional integral by delta sequence and
apply it to obtain existence-uniqueness theorems in Colombeau algebras for
nonlinear equations with singularities: nonlinear system of integral equations
with polar kernel and nonlinear parabolic equations (of ordinary type, with
nonlinear conservative term and with Schr\"odinger kernel) with strongly
singular initial data and non-Lipschitz nonlinearities. In a case of nonlinear
parabolic equations we do in fact regularization of heat semigroup with delta
sequence with respect to the time variable $t.$ We do the same for linear
Schr\"odinger equation.
