Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise

The current research deals with the exact solutions of nonlinear partial differential equations having two important difficulties, that is, coefficient singularities and stochastic function (white noise). There are four major contributions to contemporary research. One is mathematical analysis where explicit a priori estimates for existence constructed by Schauder’s fixed point theorem. Secondly, control solution behavior subject singular parameter ϵ when → 0. Thirdly, impact noise present in equation has been successfully handled solutions. final contribution simulate explain plots.