An major goal for this work is to propose a modified technique, the Elzaki Adomain Decomposition Method (ETADM), an iterative analytical approach that yields approximate analytical solutions for certain nonlinear problems. This technique relies on applying the Adomain Decomposition Method (ADM) to a nonlinear term that is amenable to solution using Adomain polynomials. ETADM has been used to break down the solution to a partial differential equation into an infinite number of components. Moreover, illustrative examples are provided, and the results obtained demonstrate the proposed method’s accuracy, efficiency, and reliability.  Results like this demonstrate how effective and efficient this method is in resolving problems of this kind. Therefore, using fractional differential equations as a model, our suggested approach can be used to analyze solutions to a broad range of genuine problems arising in the natural sciences and engineering.