A Novel Method for Solving Conformable-Order Partial Differential Equations with Applications to Real-Life Models

In this paper, an efficient methodology is employed to solve nonlinear partial differential equations of non-integer conformable order. This approach, which combines the popular Adomian decomposition method with the natural transform, can be viewed as an analytic-approximate methodology. Some conformable order partial differential equations (CPDEs) that are related to real-life phenomena such as Burgers equations and gas dynamics equation are solved using this method. Moreover, we discuss the convergence of the analytic solution that results by our proposed methodology and give an upper bound of the expected error of estimation. A nice advantage of this technique is that the exact solution is obtained in some examples. Moreover, computing the absolute errors of approximations and comparing with other methods produces very small errors with small number of iterations which indicates high accuracy. To demonstrate the effectiveness, simplicity, and correctness of our chosen method, analytical, numerical, and graphic results are provided.