Abstract
This paper presents a new approach for solving several fractional coupled systems of nonlinear partial differential equations (FCSNLPDEs) using initial conditions (ICs). This approach is based on the Elzaki transform (ET). A comprehensive description is provided to facilitate understanding of the procedure. The applicability and validity of this technique for solving FCSNLPDE problems in a few steps have been demonstrated. Using this approach, both linear and nonlinear FCSPDEs can be solved without the need for discretization or restrictive assumptions. This method requires fewer numerical calculations because it does not introduce approximation errors. Numerical examples are presented to illustrate the accuracy and efficiency of this new technique. To further illustrate how the suggested approach affected the outcomes, 2D and 3D graphs and tables were employed.