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

Abstract

In many physical processes, nonlinear PDEs have a crucial role. This paper presents a novel approach named as Modified Yang Transform (MYT) that combines an integral transform with the decomposition technique. This approach uses Yang transform and Adomian decomposition method to solve nonlinear fractional order PDEs. Nonlinear PDEs of fractional order are considered in the Caputo-Fabrizio sense. This work presents Convergence analysis of the modified Yang transform to nonlinear fractional order PDEs. Additionally, a solution framework to solve the nonlinear PDEs is carried out and some examples are provided to highlight the application of the current method.
To illustrate how the solution operates for various fractional orders, 2D and 3D graphs are plotted. After each example, the results and discussion section is included to explain the graphs and their results.