2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69353We 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 Schrödinger 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 Schrödinger equation.Analysis of PDEsFunctional Analysis46F30, 26A33, 45D05, 35K55, 35Q55text