Analyzing wave dynamics of Burger–Poisson fractional partial differential equation

Abstract

This manuscript is related to investigate fractional Burger–Poisson’s partial differential equation (FPBPDE). The aforementioned problem has many applications in wave dynamics. Because the said FPBPDE is widely used in physics, engineering, and solitary theory. More precisely, the applications encompass the study of phenomena such as solitary waves, shock waves, and various nonlinear wave behaviors across diverse physical systems. In this research paper, we have analyzed a fractional order form of the aforesaid problem containing mixed derivatives for its numerical solution. In order to evaluate the proposed problem, we have employed the Adomian decomposition method (ADM) combined with the famous Laplace transform (LT). The significant feature of this combination have been utilized very well which deals with non-linearity during the solution of non-linear differential problems (NDPs). Moreover, the non-linearity in the proposed problem has been reduced through the Adomian polynomial, and LT converts the complex differential equation into a simple algebraic form. Thus, the proposed method offers simple computational work, enabling one to obtain the desired approximate solutions for the considered non-linear FPBPDE. Furthermore, to show the simplicity and authenticity of the proposed method, we provide numerous examples. Finally, the graphical visualization for the obtained approximate solutions has been presented to demonstrate the dynamics of the obtained solutions.