Abstract
This research introduces a novel approach that combines the conformable double Laplace-Sumudu transform (CDLST) and the iterative method to handle nonlinear partial problems considering some given conditions, and we call this new approach the conformable Laplace-Sumudu iterative (CDLSI) method. Furthermore, we state and discuss the main properties and the basic results related to the proposed technique. The new method provides approximate series solutions that converge to a closed form of the exact solution. The advantage of using this method is that it produces analytical series solutions for the target equations without requiring discretization, transformation, or restricted assumptions. Moreover, we present some numerical applications to defend our results. The results demonstrate the strength and efficiency of the presented method in solving various problems in the fields of physics and engineering in symmetry with other methods.