Propagation of shock wave of the time‐fractional Gardner Burger equation in a multicomponent plasma using novel analytical method

Abstract

The time‐fractional Gardner Burger (TFGB) equation is an efficient tool for studying nonlinear fluctuations of different types of the wave profiles, such as the gravity solitary waves in the ocean and the dust ion acoustic wave (DIAW) in a plasma environment. Here, to create an example for the existence of the classical Gardner Burger (GB) equation, a multicomponent plasma environment is considered and a classical GB equation has been derived using the basic governing equation by employing reductive perturbation technique (RPT). In addition, employing Agrawal's technique, the classical GB equation is transformed to the TFGB equation by applying the Riesz fractional derivative to the time‐fractional term. To solve TFGB equations, a new approach, utilizing the improved Bernoulli subequation function method (IBSEFM), is adopted. The physical structures of the solution are explored through some two‐ and three‐dimensional figures, and the significant impact of Burgers term and fractional order of the TFGB equation are demonstrated numerically. Finally, the wave dynamics of the DIAW in the parametric space for the present plasma environment are described from the numerical understanding.