Classical Regularity and Wave Structures of Fractional Order Selkov-Schnakenberg System

Abstract

In this research article, we analyzed the fractional order Selkov-Schnakenberg system under consideration for the sake of classical regularity and analytical solutions. The existence and uniqueness of the solution of this fractional system were evaluated using self-mapping, contraction mapping, and Schauder fixed point conditions from fixed point theory in topological space. Selkov-Schnakenberg is a simple chemical reaction system in one dimension. Analytical solutions to the underlying Selkov-Schnakenberg problem were also investigated with the help of the new auxiliary equation (NAE) method. These solutions are obtained in the form of hyperbolic function, trigonometric function, and rational function which show the nature of the solution of this well-known system. The main purpose of this research is to perceive the existence and uniqueness and analytical observation of the solutions. Moreover, the physical behavior of the solutions is also dispatched via graphical 3-dim, line, and contour representation using different values of the parameters of the Selkov-Schnakenberg chemical diffusion system.