Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...

The main goal of this research is to present a new approach double transforms called the Laplace–ARA transform (DL-ARAT). This novel combination Laplace and ARA transforms. We basic properties including existence, linearity some results related partial derivatives convolution theorem. To obtain exact solutions, applied several differential equations such as Klein–Gordon equation, heat wave equa...