Applications of two kinds of Kudryashov methods for time fractional (2 + 1) dimensional Chaffee–Infante equation and its stability analysis

Abstract

In this study, the beta time fractional (2 + 1) dimensional Chaffee–Infante equation used to describe the behavior of gas diffusion in a homogeneous medium is discussed. Generalized Kudryashov and modified Kudryashov procedures were used to discovered solitons of the equation. These methods can be easily applied and offer different solutions checked to other methods in the literature. At the same time, these two methods use symbolic calculations to better understand various nonlinear wave models and offer a powerful and effective mathematical approach. The solutions created in this article are different from those in the literature and will guide those working in the field of physics and engineering to better understand this model. Figures of the results were made values different from each other. The stability of the equations in applications has been demonstrated by testing the stability feature on some solutions obtained using the features of the Hamilton system. This work demonstrates the power and effectiveness of the methods discussed in applying many different forms of fractional-order nonlinear equations. The results obtained in this paper are original to our research and have the potential to be helpful in the fields of mathematical engineering and physics.