The conformable Sumudu-Elzaki Transform Decomposition Method CSETDM is used in this research to handle the approximate numerical solutions for the regular and singular one-dimensional conformable Fractional Coupled Burger's Equation CFCBsE and the Nonlinear Singular Conformable Pseudohyperbolic equation NSCPE. This method is generalized in the sense of conformable derivatives. Essential results and theorems concerning this method are discussed. Some numerical examples are given to exhibit the proposed technique's viability, applicability, and effortlessness.