Advancing non-linear PDE's solutions: modified Yang transform method with Caputo-Fabrizio fractional operator

Abstract Nonlinear partial differential equations have a crucial rule in many physical processes. In this paper, a novel approach is used to study nonlinear partial differential equations of fractional order, which is named as Modified Yang Transform (MYT) method. This approach combines Yang transform with the Adomian decomposition method. The fractional order is considered in the Caputo-Fabrizio sense. Convergence analysis of the modified Yang transform to nonlinear fractional order partial differential equations is presented. Additionally, a solution framework for the solution of nonlinear partial differential equation is carried out and some examples are provided to highlight the application of the current method. To illustrate that how the solution behaves for various fractional orders, 2D and 3D graphs are plotted. Various tables are also provided to show the difference between exact and approximate solutions and the values are compared with other methods in the literature. Results and discussion sections are included for each example to explain the graphs, tables and their results.